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Fluid Statics
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Overview of this lecture
Calculate the forces exerted by a fluid at rest
on plane or curved submerged surfaces
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Introduction
Fluid statics: Deals with problem associated with fluids at rest.
Hydrostatics: When the fluid is a liquid.
Aerostatics: When the fluid is a gas.
In fluid statics, there is no relative motion between adjacentfluid layers, and thus there are no shear stress in the fluid
trying to deform it.
The only stress we deal with in fluid statics is the normal
stress, which is the pressure, and the variation of pressure isdue only to the weight of the fluid.
It only has significance in gravity fields.
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Introduction
The design of many engineering systems such as water dams and
liquid storage tanks requires the determination of the forcesacting on the surfaces using fluid statics.
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Hydrostatic Forces on Submerged
plane Surfaces
A plate, such as a gate valve in a dam, the wall of a liquid storage tank, orthe hull of a ship at rest, is subjected to fluid pressure distributed over its
surface when exposed to a liquid.
On a plane surface, the hydrostatic forces form a system of parallel forces,
and we often need to determine the magnitude of the force and its point
of application, which is called the center of pressure.
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General Concept:Variation of Pressure with Depth
Pressure in a fluid at rest does not change in the
horizontaldirection.
Pressure in a fluid increases linearlywith depth
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General Concept:Variation of Pressure with Depth
PA= Patm+ gh
PA= PB= PC= PD= PE= PF= PG
PH PI 7
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Hydrostatic Forces on Submerged
plane Surfaces
Recall: First moment of area
= + =
Po= Local atmospheric pressure = Patmif the liquid is open to the atmosphere
= = + = +
=1
Recall:
= + = + A
= = 8
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Hydrostatic Forces on Submerged
plane Surfaces
= =
The magnitude of the resultant force, FRacting on
a plane surface of a completely submerged plate in
a homogeneous (constant density) fluid is equal to
the product of the pressure Pcat the centroid ofthe surface and the areaAof the surface.
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Hydrostatic Forces on Submerged
plane SurfacesThe point of intersection of the line of action of the resultant force andthe surface is the center of pressure.
= = +
= +
Recall:
,=
Second moment of area
Parallel axis theorem ,= ,+ where:Ixx,c= the second moment of area about the x axis
passing through the centroid of the area
yc= the distance between two parallel axes
= + ,
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Hydrostatic Forces on Submerged
plane Surfaces
Center of pressure:
= + ,+
With atmospheric pressure applied to both
side of the plate
= + ,
The vertical distance of the center of pressure from
the free surface:
= 11
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Hydrostatic Forces on Submerged
plane Surfaces
Special case: Submerged Rectangular Plate
= + + 2
= + = + ARecall:
Recall: = + ,
+
= + 2 +
12 + 2 +
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Hydrostatic Forces on Submerged
plane Surfaces
= + + 2 = +
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=
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Example 1
A heavy car plunges into a lake during an accident and lands at the bottom of
the lake on its wheel. The door is 1.2 m high and 1 m wide, and the top edgeof the door is 8 m below the free surface of the water. Determine the
hydrostatic force on the door and the location of the pressure center and
discuss if the driver can open the door.
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Example 1 (cont.)Assumption:
1. The bottom surface of the water is horizontal/flat.
2. The passenger cabin is well-sealed so that no water leaks inside.
3. The door can be approximated as a vertical rectangular plate
4. The pressure in the passenger cabin remains at atmospheric value since
there is no water leaking in, and no compression of the air inside. (Patm
cancels out in the calculation since it acts on both sides of the door)5. The weight of the car is larger than buoyant force acting on it.
= = + = +
2
= 1000 9.81 8 + 1.22 = 84.4 /
The resultant hydrostatic force on the door:
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= = 84.4 1 1.2 = .
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Example 1 (cont.)
The pressure center is directly under the midpoint of the door:
= + 2 +
12 + 2= 8 + 1.22 +
1.21 2 8 + 1.22
= .
http://dsc.discovery.com/videos/mythbusters-underwater-car-escape-small-
scale.html
This is meant for Education purpose. The demonstrators are well-trained
individuals.
DO NOT try this at home!
Interesting Experiment
http://dsc.discovery.com/videos/mythbusters-underwater-car-escape-small-scale.htmlhttp://dsc.discovery.com/videos/mythbusters-underwater-car-escape-small-scale.htmlhttp://dsc.discovery.com/videos/mythbusters-underwater-car-escape-small-scale.htmlhttp://dsc.discovery.com/videos/mythbusters-underwater-car-escape-small-scale.htmlhttp://dsc.discovery.com/videos/mythbusters-underwater-car-escape-small-scale.htmlhttp://dsc.discovery.com/videos/mythbusters-underwater-car-escape-small-scale.htmlhttp://dsc.discovery.com/videos/mythbusters-underwater-car-escape-small-scale.htmlhttp://dsc.discovery.com/videos/mythbusters-underwater-car-escape-small-scale.htmlhttp://dsc.discovery.com/videos/mythbusters-underwater-car-escape-small-scale.htmlhttp://dsc.discovery.com/videos/mythbusters-underwater-car-escape-small-scale.htmlhttp://dsc.discovery.com/videos/mythbusters-underwater-car-escape-small-scale.htmlhttp://dsc.discovery.com/videos/mythbusters-underwater-car-escape-small-scale.htmlhttp://dsc.discovery.com/videos/mythbusters-underwater-car-escape-small-scale.html8/12/2019 W1L2 Fluid Statics
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Hydrostatic Forces on Submerged
Curved SurfacesFor submerged curved surface, the determination of the resultant force is more
complicated because it requires the integration of the pressure forces that change
direction along the curve surface.
The easier way: Determine the horizontal and vertical components, FHand FVseparately
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Hydrostatic Forces on Submerged
Curved Surfaces
Horizontal force component on curved surface:
Vertical force component on curved surface:
The magnitude of the resultant hydrostatic force acting on the curved surface:
The tangent of angle it makes with the horizontal:
=
= +
=
+
tan =19
d b d
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Hydrostatic Forces on Submerged
Curved Surfaces
When a curved surface is above the liquid,
the weight of the liquid and the vertical
component of the hydrostatic force act in the
opposite directions.
The hydrostatic force acting on a circular
surface always passes through the center
of the circle since the pressure forces are
normal to the surface and they all pass
through the center.
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Example 2 (cont.)Assumption:
1. Friction at the hinge is negligible2. Atmospheric pressure acts on both sides of the gate and thus it cancels out.
Horizontal force on vertical surface:
Vertical force on horizontal surface:
= = = = +
2
= 1000 9.81 4.2+ 0.82 0.8 1 = 36.1
= = =
= 1000 9.81 (5 ) 0.8 1 = 39.2
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Example 2 (cont.)
Weight of the fluid block:
= = = 4 1
= 1000 9.81 0.8 2 1
4 (1 ) = 1.3
= = 39.2 1.3 = 37.9 The net upward vertical force:
= += 36.1+ 37.9= . tan = =
37.936.1= 1.05 = .
The resultant force:
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Example 2 (cont.)
(b) When the water level is 5 m high, the gate is about to open and thus the reaction
force at the bottom of the cylinder is zero. Then the forces other than those at thehinge acting on the cylinder are its weight, acting through the center and hydrostatic
force exerted by water. Taking a moment about point A and equating it to zero.
= 0 = = 52.3 (sin46.4) = .
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Example 3 (cont.)
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Example 3 (cont.)
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What You Learned from
FLUID STATICS
Hydrostatic force on submerged surfaces
Center of pressure
Reading Material: Y. A. Cengel, J. M. Cimbala, R. H. Turner, Fundamentals of
Thermal-fluid Sciences, 4thed. Chapter 11.
Next Lecture: Fluid Power System- Hydraulic system
- Pneumatic system
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End of Lecture
Q & A
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