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Fluid Mechanics and Thermodynamics Weekly Assessed Tutorial Sheets, Student Sheets
The WATS approach to assessment was developed as part of an LTSN Engineering Mini-Project, funded at the University of Hertfordshire which aimed to develop a set of 'student unique' tutorial sheets to actively encourage and improve student participation within a first year first „fluid mechanics and thermodynamics‟ module. Please see the accompanying Mini-Project Report “Improving student success and retention through greater participation and tackling student-unique tutorial sheets” for more information.
The WATS cover core Fluid Mechanics and Thermodynamics topics at first year undergraduate level. 11 tutorial sheets and their worked solutions are provided here for you to utilise in your teaching. The variables within each question can be altered so that each student answers the same question but will need to produce a unique solution.
What follows is a set of STUDENT UNIQUE SHEETS for WATS 8.
For more information on WATS, its use and impact on students please contact Mark Russell, School of Aerospace, Automotive and Design Engineering at University of Hertfordshire.
W|ATS8 Student number 1
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 1
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Q1a). A fluid of relative density 0.91 flows through a pipe of diameter 100 mm at 0.19 m/s. After
passing through a gradual reducer the fluid leaves a 33mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 10° (net force)
(N) [5dp] (2
Mark)
iii) A = 57° (Net force)
(N) [5dp] (2
Mark)
iv) A = 79° (Net force)
(N) [5dp] (2
Mark)
Q2. 9 l/s flows through a contracting elbow which has an angle, ‘A’ of 34° i.e. as shown in
figure Q2. Assume the inlet to the bend is 225 mm diameter and the outlet is 90 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 4.60 Bar
and the fluids specific gravity is 0.96. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 2
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 2
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Q1a). A fluid of relative density 0.86 flows through a pipe of diameter 85 mm at 0.18 m/s. After
passing through a gradual reducer the fluid leaves a 46mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 21° (net force)
(N) [5dp] (2
Mark)
iii) A = 63° (Net force)
(N) [5dp] (2
Mark)
iv) A = 85° (Net force)
(N) [5dp] (2
Mark)
Q2. 5 l/s flows through a contracting elbow which has an angle, ‘A’ of 58° i.e. as shown in
figure Q2. Assume the inlet to the bend is 280 mm diameter and the outlet is 65 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 2.90 Bar
and the fluids specific gravity is 0.92. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 3
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 3
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Q1a). A fluid of relative density 0.95 flows through a pipe of diameter 80 mm at 0.30 m/s. After
passing through a gradual reducer the fluid leaves a 29mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 18° (net force)
(N) [5dp] (2
Mark)
iii) A = 44° (Net force)
(N) [5dp] (2
Mark)
iv) A = 85° (Net force)
(N) [5dp] (2
Mark)
Q2. 7 l/s flows through a contracting elbow which has an angle, ‘A’ of 70° i.e. as shown in
figure Q2. Assume the inlet to the bend is 165 mm diameter and the outlet is 125 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
1.80 Bar and the fluids specific gravity is 0.85. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 4
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 4
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Q1a). A fluid of relative density 0.95 flows through a pipe of diameter 125 mm at 0.14 m/s. After
passing through a gradual reducer the fluid leaves a 66mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 21° (net force)
(N) [5dp] (2
Mark)
iii) A = 55° (Net force)
(N) [5dp] (2
Mark)
iv) A = 81° (Net force)
(N) [5dp] (2
Mark)
Q2. 6 l/s flows through a contracting elbow which has an angle, ‘A’ of 12° i.e. as shown in
figure Q2. Assume the inlet to the bend is 190 mm diameter and the outlet is 75 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.70 Bar
and the fluids specific gravity is 0.82. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 5
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 5
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Q1a). A fluid of relative density 0.94 flows through a pipe of diameter 90 mm at 0.29 m/s. After
passing through a gradual reducer the fluid leaves a 26mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 27° (net force)
(N) [5dp] (2
Mark)
iii) A = 54° (Net force)
(N) [5dp] (2
Mark)
iv) A = 78° (Net force)
(N) [5dp] (2
Mark)
Q2. 15 l/s flows through a contracting elbow which has an angle, ‘A’ of 39° i.e. as shown in
figure Q2. Assume the inlet to the bend is 270 mm diameter and the outlet is 75 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 1.90 Bar
and the fluids specific gravity is 0.80. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 6
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 6
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Q1a). A fluid of relative density 0.88 flows through a pipe of diameter 110 mm at 0.47 m/s. After
passing through a gradual reducer the fluid leaves a 72mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 20° (net force)
(N) [5dp] (2
Mark)
iii) A = 56° (Net force)
(N) [5dp] (2
Mark)
iv) A = 78° (Net force)
(N) [5dp] (2
Mark)
Q2. 10 l/s flows through a contracting elbow which has an angle, ‘A’ of 37° i.e. as shown in
figure Q2. Assume the inlet to the bend is 275 mm diameter and the outlet is 60 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.70 Bar
and the fluids specific gravity is 0.78. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 7
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 7
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Q1a). A fluid of relative density 0.96 flows through a pipe of diameter 105 mm at 0.41 m/s. After
passing through a gradual reducer the fluid leaves a 44mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 7° (net force)
(N) [5dp] (2
Mark)
iii) A = 46° (Net force)
(N) [5dp] (2
Mark)
iv) A = 68° (Net force)
(N) [5dp] (2
Mark)
Q2. 4 l/s flows through a contracting elbow which has an angle, ‘A’ of 13° i.e. as shown in
figure Q2. Assume the inlet to the bend is 195 mm diameter and the outlet is 75 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.80 Bar
and the fluids specific gravity is 0.86. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 8
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 8
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Q1a). A fluid of relative density 0.99 flows through a pipe of diameter 130 mm at 0.21 m/s. After
passing through a gradual reducer the fluid leaves a 69mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 19° (net force)
(N) [5dp] (2
Mark)
iii) A = 59° (Net force)
(N) [5dp] (2
Mark)
iv) A = 74° (Net force)
(N) [5dp] (2
Mark)
Q2. 9 l/s flows through a contracting elbow which has an angle, ‘A’ of 38° i.e. as shown in
figure Q2. Assume the inlet to the bend is 300 mm diameter and the outlet is 70 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 2.10 Bar
and the fluids specific gravity is 0.90. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 9
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 9
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Q1a). A fluid of relative density 0.81 flows through a pipe of diameter 135 mm at 0.25 m/s. After
passing through a gradual reducer the fluid leaves a 65mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 25° (net force)
(N) [5dp] (2
Mark)
iii) A = 36° (Net force)
(N) [5dp] (2
Mark)
iv) A = 77° (Net force)
(N) [5dp] (2
Mark)
Q2. 6 l/s flows through a contracting elbow which has an angle, ‘A’ of 38° i.e. as shown in
figure Q2. Assume the inlet to the bend is 220 mm diameter and the outlet is 70 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.70 Bar
and the fluids specific gravity is 0.76. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 10
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 10
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Q1a). A fluid of relative density 0.87 flows through a pipe of diameter 85 mm at 0.08 m/s. After
passing through a gradual reducer the fluid leaves a 36mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 33° (net force)
(N) [5dp] (2
Mark)
iii) A = 48° (Net force)
(N) [5dp] (2
Mark)
iv) A = 80° (Net force)
(N) [5dp] (2
Mark)
Q2. 10 l/s flows through a contracting elbow which has an angle, ‘A’ of 51° i.e. as shown in
figure Q2. Assume the inlet to the bend is 165 mm diameter and the outlet is 140 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
2.00 Bar and the fluids specific gravity is 0.79. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 11
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 11
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Q1a). A fluid of relative density 0.95 flows through a pipe of diameter 85 mm at 0.10 m/s. After
passing through a gradual reducer the fluid leaves a 70mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 4° (net force)
(N) [5dp] (2
Mark)
iii) A = 56° (Net force)
(N) [5dp] (2
Mark)
iv) A = 64° (Net force)
(N) [5dp] (2
Mark)
Q2. 3 l/s flows through a contracting elbow which has an angle, ‘A’ of 38° i.e. as shown in
figure Q2. Assume the inlet to the bend is 290 mm diameter and the outlet is 115 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
1.40 Bar and the fluids specific gravity is 0.88. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 12
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 12
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Q1a). A fluid of relative density 0.92 flows through a pipe of diameter 90 mm at 0.34 m/s. After
passing through a gradual reducer the fluid leaves a 58mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 26° (net force)
(N) [5dp] (2
Mark)
iii) A = 44° (Net force)
(N) [5dp] (2
Mark)
iv) A = 71° (Net force)
(N) [5dp] (2
Mark)
Q2. 9 l/s flows through a contracting elbow which has an angle, ‘A’ of 78° i.e. as shown in
figure Q2. Assume the inlet to the bend is 175 mm diameter and the outlet is 105 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
2.00 Bar and the fluids specific gravity is 0.76. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 13
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 13
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Q1a). A fluid of relative density 0.86 flows through a pipe of diameter 140 mm at 0.33 m/s. After
passing through a gradual reducer the fluid leaves a 26mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 11° (net force)
(N) [5dp] (2
Mark)
iii) A = 38° (Net force)
(N) [5dp] (2
Mark)
iv) A = 78° (Net force)
(N) [5dp] (2
Mark)
Q2. 7 l/s flows through a contracting elbow which has an angle, ‘A’ of 22° i.e. as shown in
figure Q2. Assume the inlet to the bend is 185 mm diameter and the outlet is 130 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
4.30 Bar and the fluids specific gravity is 0.96. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 14
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 14
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Q1a). A fluid of relative density 0.93 flows through a pipe of diameter 130 mm at 0.39 m/s. After
passing through a gradual reducer the fluid leaves a 35mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 6° (net force)
(N) [5dp] (2
Mark)
iii) A = 52° (Net force)
(N) [5dp] (2
Mark)
iv) A = 80° (Net force)
(N) [5dp] (2
Mark)
Q2. 14 l/s flows through a contracting elbow which has an angle, ‘A’ of 25° i.e. as shown in
figure Q2. Assume the inlet to the bend is 270 mm diameter and the outlet is 50 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.30 Bar
and the fluids specific gravity is 0.83. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 15
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 15
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Q1a). A fluid of relative density 0.86 flows through a pipe of diameter 95 mm at 0.05 m/s. After
passing through a gradual reducer the fluid leaves a 47mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 27° (net force)
(N) [5dp] (2
Mark)
iii) A = 46° (Net force)
(N) [5dp] (2
Mark)
iv) A = 84° (Net force)
(N) [5dp] (2
Mark)
Q2. 3 l/s flows through a contracting elbow which has an angle, ‘A’ of 20° i.e. as shown in
figure Q2. Assume the inlet to the bend is 245 mm diameter and the outlet is 65 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 4.00 Bar
and the fluids specific gravity is 0.87. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 16
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 16
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Q1a). A fluid of relative density 0.96 flows through a pipe of diameter 135 mm at 0.29 m/s. After
passing through a gradual reducer the fluid leaves a 39mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 26° (net force)
(N) [5dp] (2
Mark)
iii) A = 40° (Net force)
(N) [5dp] (2
Mark)
iv) A = 64° (Net force)
(N) [5dp] (2
Mark)
Q2. 11 l/s flows through a contracting elbow which has an angle, ‘A’ of 68° i.e. as shown in
figure Q2. Assume the inlet to the bend is 230 mm diameter and the outlet is 140 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
3.70 Bar and the fluids specific gravity is 0.82. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 17
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 17
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Q1a). A fluid of relative density 1.00 flows through a pipe of diameter 135 mm at 0.21 m/s. After
passing through a gradual reducer the fluid leaves a 67mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 17° (net force)
(N) [5dp] (2
Mark)
iii) A = 60° (Net force)
(N) [5dp] (2
Mark)
iv) A = 79° (Net force)
(N) [5dp] (2
Mark)
Q2. 15 l/s flows through a contracting elbow which has an angle, ‘A’ of 41° i.e. as shown in
figure Q2. Assume the inlet to the bend is 260 mm diameter and the outlet is 130 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
1.60 Bar and the fluids specific gravity is 0.99. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 18
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 18
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Q1a). A fluid of relative density 0.85 flows through a pipe of diameter 110 mm at 0.08 m/s. After
passing through a gradual reducer the fluid leaves a 42mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 23° (net force)
(N) [5dp] (2
Mark)
iii) A = 37° (Net force)
(N) [5dp] (2
Mark)
iv) A = 79° (Net force)
(N) [5dp] (2
Mark)
Q2. 11 l/s flows through a contracting elbow which has an angle, ‘A’ of 56° i.e. as shown in
figure Q2. Assume the inlet to the bend is 205 mm diameter and the outlet is 130 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
3.00 Bar and the fluids specific gravity is 0.91. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 19
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 19
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Q1a). A fluid of relative density 1.00 flows through a pipe of diameter 135 mm at 0.50 m/s. After
passing through a gradual reducer the fluid leaves a 67mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 8° (net force)
(N) [5dp] (2
Mark)
iii) A = 47° (Net force)
(N) [5dp] (2
Mark)
iv) A = 69° (Net force)
(N) [5dp] (2
Mark)
Q2. 15 l/s flows through a contracting elbow which has an angle, ‘A’ of 50° i.e. as shown in
figure Q2. Assume the inlet to the bend is 160 mm diameter and the outlet is 120 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
2.10 Bar and the fluids specific gravity is 0.83. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 20
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 20
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Q1a). A fluid of relative density 0.91 flows through a pipe of diameter 90 mm at 0.14 m/s. After
passing through a gradual reducer the fluid leaves a 54mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 22° (net force)
(N) [5dp] (2
Mark)
iii) A = 42° (Net force)
(N) [5dp] (2
Mark)
iv) A = 66° (Net force)
(N) [5dp] (2
Mark)
Q2. 4 l/s flows through a contracting elbow which has an angle, ‘A’ of 61° i.e. as shown in
figure Q2. Assume the inlet to the bend is 230 mm diameter and the outlet is 80 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 2.30 Bar
and the fluids specific gravity is 0.93. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 21
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 21
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Q1a). A fluid of relative density 1.00 flows through a pipe of diameter 100 mm at 0.24 m/s. After
passing through a gradual reducer the fluid leaves a 71mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 26° (net force)
(N) [5dp] (2
Mark)
iii) A = 52° (Net force)
(N) [5dp] (2
Mark)
iv) A = 84° (Net force)
(N) [5dp] (2
Mark)
Q2. 7 l/s flows through a contracting elbow which has an angle, ‘A’ of 28° i.e. as shown in
figure Q2. Assume the inlet to the bend is 290 mm diameter and the outlet is 140 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
2.40 Bar and the fluids specific gravity is 0.77. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 22
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 22
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Q1a). A fluid of relative density 0.80 flows through a pipe of diameter 100 mm at 0.23 m/s. After
passing through a gradual reducer the fluid leaves a 26mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 14° (net force)
(N) [5dp] (2
Mark)
iii) A = 55° (Net force)
(N) [5dp] (2
Mark)
iv) A = 79° (Net force)
(N) [5dp] (2
Mark)
Q2. 4 l/s flows through a contracting elbow which has an angle, ‘A’ of 24° i.e. as shown in
figure Q2. Assume the inlet to the bend is 205 mm diameter and the outlet is 75 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 4.20 Bar
and the fluids specific gravity is 0.78. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 23
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 23
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Q1a). A fluid of relative density 0.82 flows through a pipe of diameter 105 mm at 0.47 m/s. After
passing through a gradual reducer the fluid leaves a 54mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 13° (net force)
(N) [5dp] (2
Mark)
iii) A = 50° (Net force)
(N) [5dp] (2
Mark)
iv) A = 68° (Net force)
(N) [5dp] (2
Mark)
Q2. 7 l/s flows through a contracting elbow which has an angle, ‘A’ of 52° i.e. as shown in
figure Q2. Assume the inlet to the bend is 235 mm diameter and the outlet is 65 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.70 Bar
and the fluids specific gravity is 0.86. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 24
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Student Number 24
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Q1a). A fluid of relative density 0.96 flows through a pipe of diameter 80 mm at 0.10 m/s. After
passing through a gradual reducer the fluid leaves a 56mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 26° (net force)
(N) [5dp] (2
Mark)
iii) A = 51° (Net force)
(N) [5dp] (2
Mark)
iv) A = 68° (Net force)
(N) [5dp] (2
Mark)
Q2. 5 l/s flows through a contracting elbow which has an angle, ‘A’ of 57° i.e. as shown in
figure Q2. Assume the inlet to the bend is 270 mm diameter and the outlet is 55 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 1.60 Bar
and the fluids specific gravity is 0.76. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 25
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 25
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Q1a). A fluid of relative density 0.81 flows through a pipe of diameter 90 mm at 0.18 m/s. After
passing through a gradual reducer the fluid leaves a 60mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 15° (net force)
(N) [5dp] (2
Mark)
iii) A = 48° (Net force)
(N) [5dp] (2
Mark)
iv) A = 71° (Net force)
(N) [5dp] (2
Mark)
Q2. 8 l/s flows through a contracting elbow which has an angle, ‘A’ of 43° i.e. as shown in
figure Q2. Assume the inlet to the bend is 235 mm diameter and the outlet is 130 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
1.20 Bar and the fluids specific gravity is 0.91. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 26
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 26
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Q1a). A fluid of relative density 0.88 flows through a pipe of diameter 145 mm at 0.20 m/s. After
passing through a gradual reducer the fluid leaves a 28mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 14° (net force)
(N) [5dp] (2
Mark)
iii) A = 58° (Net force)
(N) [5dp] (2
Mark)
iv) A = 67° (Net force)
(N) [5dp] (2
Mark)
Q2. 13 l/s flows through a contracting elbow which has an angle, ‘A’ of 55° i.e. as shown in
figure Q2. Assume the inlet to the bend is 250 mm diameter and the outlet is 65 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.80 Bar
and the fluids specific gravity is 0.75. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 27
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 27
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Q1a). A fluid of relative density 0.99 flows through a pipe of diameter 140 mm at 0.04 m/s. After
passing through a gradual reducer the fluid leaves a 35mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 24° (net force)
(N) [5dp] (2
Mark)
iii) A = 46° (Net force)
(N) [5dp] (2
Mark)
iv) A = 83° (Net force)
(N) [5dp] (2
Mark)
Q2. 12 l/s flows through a contracting elbow which has an angle, ‘A’ of 22° i.e. as shown in
figure Q2. Assume the inlet to the bend is 220 mm diameter and the outlet is 70 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 2.00 Bar
and the fluids specific gravity is 0.88. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 28
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 28
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Q1a). A fluid of relative density 0.88 flows through a pipe of diameter 135 mm at 0.19 m/s. After
passing through a gradual reducer the fluid leaves a 34mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 9° (net force)
(N) [5dp] (2
Mark)
iii) A = 59° (Net force)
(N) [5dp] (2
Mark)
iv) A = 79° (Net force)
(N) [5dp] (2
Mark)
Q2. 14 l/s flows through a contracting elbow which has an angle, ‘A’ of 34° i.e. as shown in
figure Q2. Assume the inlet to the bend is 250 mm diameter and the outlet is 50 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 4.00 Bar
and the fluids specific gravity is 0.86. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 29
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 29
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Q1a). A fluid of relative density 0.83 flows through a pipe of diameter 95 mm at 0.44 m/s. After
passing through a gradual reducer the fluid leaves a 70mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 31° (net force)
(N) [5dp] (2
Mark)
iii) A = 62° (Net force)
(N) [5dp] (2
Mark)
iv) A = 73° (Net force)
(N) [5dp] (2
Mark)
Q2. 7 l/s flows through a contracting elbow which has an angle, ‘A’ of 29° i.e. as shown in
figure Q2. Assume the inlet to the bend is 260 mm diameter and the outlet is 110 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
1.50 Bar and the fluids specific gravity is 0.87. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 30
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 30
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Q1a). A fluid of relative density 0.93 flows through a pipe of diameter 125 mm at 0.30 m/s. After
passing through a gradual reducer the fluid leaves a 38mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 26° (net force)
(N) [5dp] (2
Mark)
iii) A = 53° (Net force)
(N) [5dp] (2
Mark)
iv) A = 75° (Net force)
(N) [5dp] (2
Mark)
Q2. 7 l/s flows through a contracting elbow which has an angle, ‘A’ of 59° i.e. as shown in
figure Q2. Assume the inlet to the bend is 175 mm diameter and the outlet is 115 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
2.80 Bar and the fluids specific gravity is 0.94. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 31
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 31
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Q1a). A fluid of relative density 0.88 flows through a pipe of diameter 100 mm at 0.04 m/s. After
passing through a gradual reducer the fluid leaves a 62mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 7° (net force)
(N) [5dp] (2
Mark)
iii) A = 46° (Net force)
(N) [5dp] (2
Mark)
iv) A = 86° (Net force)
(N) [5dp] (2
Mark)
Q2. 6 l/s flows through a contracting elbow which has an angle, ‘A’ of 68° i.e. as shown in
figure Q2. Assume the inlet to the bend is 265 mm diameter and the outlet is 70 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.60 Bar
and the fluids specific gravity is 0.92. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 32
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 32
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Q1a). A fluid of relative density 0.87 flows through a pipe of diameter 85 mm at 0.08 m/s. After
passing through a gradual reducer the fluid leaves a 33mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 10° (net force)
(N) [5dp] (2
Mark)
iii) A = 34° (Net force)
(N) [5dp] (2
Mark)
iv) A = 67° (Net force)
(N) [5dp] (2
Mark)
Q2. 10 l/s flows through a contracting elbow which has an angle, ‘A’ of 54° i.e. as shown in
figure Q2. Assume the inlet to the bend is 255 mm diameter and the outlet is 95 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 1.30 Bar
and the fluids specific gravity is 0.88. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 33
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 33
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Q1a). A fluid of relative density 0.84 flows through a pipe of diameter 95 mm at 0.38 m/s. After
passing through a gradual reducer the fluid leaves a 31mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 26° (net force)
(N) [5dp] (2
Mark)
iii) A = 44° (Net force)
(N) [5dp] (2
Mark)
iv) A = 71° (Net force)
(N) [5dp] (2
Mark)
Q2. 8 l/s flows through a contracting elbow which has an angle, ‘A’ of 59° i.e. as shown in
figure Q2. Assume the inlet to the bend is 210 mm diameter and the outlet is 50 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 2.40 Bar
and the fluids specific gravity is 0.82. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 34
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 34
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Q1a). A fluid of relative density 0.92 flows through a pipe of diameter 115 mm at 0.08 m/s. After
passing through a gradual reducer the fluid leaves a 67mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 6° (net force)
(N) [5dp] (2
Mark)
iii) A = 61° (Net force)
(N) [5dp] (2
Mark)
iv) A = 77° (Net force)
(N) [5dp] (2
Mark)
Q2. 12 l/s flows through a contracting elbow which has an angle, ‘A’ of 49° i.e. as shown in
figure Q2. Assume the inlet to the bend is 185 mm diameter and the outlet is 80 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.50 Bar
and the fluids specific gravity is 0.79. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 35
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 35
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Q1a). A fluid of relative density 0.89 flows through a pipe of diameter 95 mm at 0.35 m/s. After
passing through a gradual reducer the fluid leaves a 48mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 23° (net force)
(N) [5dp] (2
Mark)
iii) A = 62° (Net force)
(N) [5dp] (2
Mark)
iv) A = 73° (Net force)
(N) [5dp] (2
Mark)
Q2. 3 l/s flows through a contracting elbow which has an angle, ‘A’ of 25° i.e. as shown in
figure Q2. Assume the inlet to the bend is 220 mm diameter and the outlet is 110 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
4.20 Bar and the fluids specific gravity is 0.80. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 36
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 36
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Q1a). A fluid of relative density 0.85 flows through a pipe of diameter 100 mm at 0.26 m/s. After
passing through a gradual reducer the fluid leaves a 36mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 28° (net force)
(N) [5dp] (2
Mark)
iii) A = 53° (Net force)
(N) [5dp] (2
Mark)
iv) A = 84° (Net force)
(N) [5dp] (2
Mark)
Q2. 4 l/s flows through a contracting elbow which has an angle, ‘A’ of 20° i.e. as shown in
figure Q2. Assume the inlet to the bend is 170 mm diameter and the outlet is 90 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.40 Bar
and the fluids specific gravity is 0.87. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 37
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 37
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Q1a). A fluid of relative density 0.88 flows through a pipe of diameter 105 mm at 0.49 m/s. After
passing through a gradual reducer the fluid leaves a 38mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 22° (net force)
(N) [5dp] (2
Mark)
iii) A = 41° (Net force)
(N) [5dp] (2
Mark)
iv) A = 77° (Net force)
(N) [5dp] (2
Mark)
Q2. 15 l/s flows through a contracting elbow which has an angle, ‘A’ of 16° i.e. as shown in
figure Q2. Assume the inlet to the bend is 270 mm diameter and the outlet is 70 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 4.00 Bar
and the fluids specific gravity is 0.99. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 38
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 38
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Q1a). A fluid of relative density 0.98 flows through a pipe of diameter 105 mm at 0.04 m/s. After
passing through a gradual reducer the fluid leaves a 28mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 30° (net force)
(N) [5dp] (2
Mark)
iii) A = 44° (Net force)
(N) [5dp] (2
Mark)
iv) A = 70° (Net force)
(N) [5dp] (2
Mark)
Q2. 3 l/s flows through a contracting elbow which has an angle, ‘A’ of 34° i.e. as shown in
figure Q2. Assume the inlet to the bend is 165 mm diameter and the outlet is 95 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 4.60 Bar
and the fluids specific gravity is 0.98. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 39
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 39
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Q1a). A fluid of relative density 0.93 flows through a pipe of diameter 125 mm at 0.17 m/s. After
passing through a gradual reducer the fluid leaves a 29mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 28° (net force)
(N) [5dp] (2
Mark)
iii) A = 63° (Net force)
(N) [5dp] (2
Mark)
iv) A = 75° (Net force)
(N) [5dp] (2
Mark)
Q2. 3 l/s flows through a contracting elbow which has an angle, ‘A’ of 45° i.e. as shown in
figure Q2. Assume the inlet to the bend is 180 mm diameter and the outlet is 95 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 1.40 Bar
and the fluids specific gravity is 0.97. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 40
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 40
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Q1a). A fluid of relative density 0.82 flows through a pipe of diameter 145 mm at 0.34 m/s. After
passing through a gradual reducer the fluid leaves a 38mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 7° (net force)
(N) [5dp] (2
Mark)
iii) A = 52° (Net force)
(N) [5dp] (2
Mark)
iv) A = 72° (Net force)
(N) [5dp] (2
Mark)
Q2. 9 l/s flows through a contracting elbow which has an angle, ‘A’ of 56° i.e. as shown in
figure Q2. Assume the inlet to the bend is 215 mm diameter and the outlet is 130 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
1.70 Bar and the fluids specific gravity is 0.93. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 41
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 41
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Q1a). A fluid of relative density 0.94 flows through a pipe of diameter 115 mm at 0.20 m/s. After
passing through a gradual reducer the fluid leaves a 28mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 5° (net force)
(N) [5dp] (2
Mark)
iii) A = 38° (Net force)
(N) [5dp] (2
Mark)
iv) A = 77° (Net force)
(N) [5dp] (2
Mark)
Q2. 7 l/s flows through a contracting elbow which has an angle, ‘A’ of 52° i.e. as shown in
figure Q2. Assume the inlet to the bend is 295 mm diameter and the outlet is 70 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 2.10 Bar
and the fluids specific gravity is 0.84. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 42
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
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Q1a). A fluid of relative density 0.97 flows through a pipe of diameter 120 mm at 0.44 m/s. After
passing through a gradual reducer the fluid leaves a 49mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 7° (net force)
(N) [5dp] (2
Mark)
iii) A = 62° (Net force)
(N) [5dp] (2
Mark)
iv) A = 81° (Net force)
(N) [5dp] (2
Mark)
Q2. 10 l/s flows through a contracting elbow which has an angle, ‘A’ of 55° i.e. as shown in
figure Q2. Assume the inlet to the bend is 235 mm diameter and the outlet is 60 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 2.20 Bar
and the fluids specific gravity is 0.84. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 43
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 43
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Q1a). A fluid of relative density 0.91 flows through a pipe of diameter 110 mm at 0.21 m/s. After
passing through a gradual reducer the fluid leaves a 47mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 13° (net force)
(N) [5dp] (2
Mark)
iii) A = 51° (Net force)
(N) [5dp] (2
Mark)
iv) A = 80° (Net force)
(N) [5dp] (2
Mark)
Q2. 15 l/s flows through a contracting elbow which has an angle, ‘A’ of 80° i.e. as shown in
figure Q2. Assume the inlet to the bend is 240 mm diameter and the outlet is 125 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
4.90 Bar and the fluids specific gravity is 0.91. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 44
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 44
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Q1a). A fluid of relative density 0.89 flows through a pipe of diameter 95 mm at 0.28 m/s. After
passing through a gradual reducer the fluid leaves a 65mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 5° (net force)
(N) [5dp] (2
Mark)
iii) A = 47° (Net force)
(N) [5dp] (2
Mark)
iv) A = 81° (Net force)
(N) [5dp] (2
Mark)
Q2. 13 l/s flows through a contracting elbow which has an angle, ‘A’ of 58° i.e. as shown in
figure Q2. Assume the inlet to the bend is 265 mm diameter and the outlet is 110 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
1.80 Bar and the fluids specific gravity is 0.86. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 45
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 45
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Q1a). A fluid of relative density 0.90 flows through a pipe of diameter 140 mm at 0.07 m/s. After
passing through a gradual reducer the fluid leaves a 53mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 31° (net force)
(N) [5dp] (2
Mark)
iii) A = 58° (Net force)
(N) [5dp] (2
Mark)
iv) A = 87° (Net force)
(N) [5dp] (2
Mark)
Q2. 15 l/s flows through a contracting elbow which has an angle, ‘A’ of 63° i.e. as shown in
figure Q2. Assume the inlet to the bend is 210 mm diameter and the outlet is 75 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 1.40 Bar
and the fluids specific gravity is 0.90. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 46
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 46
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Q1a). A fluid of relative density 0.89 flows through a pipe of diameter 105 mm at 0.01 m/s. After
passing through a gradual reducer the fluid leaves a 64mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 24° (net force)
(N) [5dp] (2
Mark)
iii) A = 59° (Net force)
(N) [5dp] (2
Mark)
iv) A = 72° (Net force)
(N) [5dp] (2
Mark)
Q2. 12 l/s flows through a contracting elbow which has an angle, ‘A’ of 11° i.e. as shown in
figure Q2. Assume the inlet to the bend is 195 mm diameter and the outlet is 50 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 4.20 Bar
and the fluids specific gravity is 0.89. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 47
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 47
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Hand out date Hand in date
Q1a). A fluid of relative density 0.88 flows through a pipe of diameter 95 mm at 0.46 m/s. After
passing through a gradual reducer the fluid leaves a 73mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 15° (net force)
(N) [5dp] (2
Mark)
iii) A = 45° (Net force)
(N) [5dp] (2
Mark)
iv) A = 65° (Net force)
(N) [5dp] (2
Mark)
Q2. 8 l/s flows through a contracting elbow which has an angle, ‘A’ of 47° i.e. as shown in
figure Q2. Assume the inlet to the bend is 290 mm diameter and the outlet is 80 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.40 Bar
and the fluids specific gravity is 0.98. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 48
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 48
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Q1a). A fluid of relative density 0.81 flows through a pipe of diameter 130 mm at 0.12 m/s. After
passing through a gradual reducer the fluid leaves a 58mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 23° (net force)
(N) [5dp] (2
Mark)
iii) A = 59° (Net force)
(N) [5dp] (2
Mark)
iv) A = 75° (Net force)
(N) [5dp] (2
Mark)
Q2. 14 l/s flows through a contracting elbow which has an angle, ‘A’ of 76° i.e. as shown in
figure Q2. Assume the inlet to the bend is 225 mm diameter and the outlet is 125 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
2.50 Bar and the fluids specific gravity is 0.96. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 49
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 49
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Q1a). A fluid of relative density 1.00 flows through a pipe of diameter 120 mm at 0.10 m/s. After
passing through a gradual reducer the fluid leaves a 61mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 32° (net force)
(N) [5dp] (2
Mark)
iii) A = 61° (Net force)
(N) [5dp] (2
Mark)
iv) A = 72° (Net force)
(N) [5dp] (2
Mark)
Q2. 9 l/s flows through a contracting elbow which has an angle, ‘A’ of 73° i.e. as shown in
figure Q2. Assume the inlet to the bend is 190 mm diameter and the outlet is 110 mm
diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is
2.10 Bar and the fluids specific gravity is 0.90. Calculate the net force and the direction of the
force acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
W|ATS8 Student number 50
Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.
Student Number 50
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Hand out date Hand in date
Q1a). A fluid of relative density 0.88 flows through a pipe of diameter 115 mm at 0.19 m/s. After
passing through a gradual reducer the fluid leaves a 73mm diameter pipe and discharges onto a
stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal
plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected
along its surface - calculate the forces acting on the surface for the angles shown in the
answer boxes. You may assume that friction effects are negligible.
Figure Q1a. Definition of angle ‘A’ for the inclined surface.
i) A = 90° (X force)
(N) [5dp] (1
Mark)
ii) A = 31° (net force)
(N) [5dp] (2
Mark)
iii) A = 51° (Net force)
(N) [5dp] (2
Mark)
iv) A = 79° (Net force)
(N) [5dp] (2
Mark)
Q2. 8 l/s flows through a contracting elbow which has an angle, ‘A’ of 40° i.e. as shown in
figure Q2. Assume the inlet to the bend is 215 mm diameter and the outlet is 95 mm diameter
and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 4.60 Bar
and the fluids specific gravity is 0.79. Calculate the net force and the direction of the force
acting on the bend.
i) Net force (N)
[5dp]
(3 Mark)
ii) Direction of force.
(As measured anti-clockwise from the
top of the horizontal plane. i.e. AS
SHOWN in all above examples. [1dp]
(1 Mark)
Figure Q2. Sketch of bend.
90.0°
A X
Y
45.5°
A
Y
X
52.2°
A
X
Y
_______________________________________________________________________________________________
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© University of Hertfordshire 2009
This work is licensed under a Creative Commons Attribution 2.0 License. The name of the University of Hertfordshire, UH and the UH logo are the name and registered marks of the University of Hertfordshire. To the fullest extent permitted by law the University of Hertfordshire reserves all its rights in its name and marks which may not be used except with its written permission. The JISC logo is licensed under the terms of the Creative Commons Attribution-Non-Commercial-No Derivative Works 2.0 UK: England & Wales Licence. All reproductions must comply with the terms of that licence. The HEA logo is owned by the Higher Education Academy Limited may be freely distributed and copied for educational purposes only, provided that appropriate acknowledgement is given to the Higher Education Academy as the copyright holder and original publisher.
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