Hydrodynamics

HydrodynamicsHydrodynamics

Hydrodynamics is a branch of Hydrodynamics is a branch of physics that studies about the physics that studies about the motion of fluid.motion of fluid.

Ideal Fluid has properties : Ideal Fluid has properties : incompresible and its flow in incompresible and its flow in either steady or laminer.either steady or laminer.

Incompresible means that the Incompresible means that the density of the fluid does not density of the fluid does not depend on the pressure, it can depend on the pressure, it can not be compressed.not be compressed.

A steady flow means that the A steady flow means that the particle’s motion follows a particle’s motion follows a same flow line. same flow line.

The Equation of ContinuityThe Equation of Continuity Volume flow rate (Q) is defined as the amount (volume) of fluid flow Volume flow rate (Q) is defined as the amount (volume) of fluid flow

per time unitper time unit Q = V/tQ = V/t For incompresible fluid, the volume flow rate is the same at any For incompresible fluid, the volume flow rate is the same at any

point in the fluidpoint in the fluid AA11vv11 = A = A22vv2 2 or Q or Q11 = Q = Q22

Equation above is called continuity equation which states that : at Equation above is called continuity equation which states that : at any points in fluid, the rate of volume flow is constant. The speed of any points in fluid, the rate of volume flow is constant. The speed of flow will be greater if it passes the smaller cross-sectionalflow will be greater if it passes the smaller cross-sectional

Student ActivityStudent Activity

The average velocity of water flow in a The average velocity of water flow in a pipe with diameter 4 cm is 4 m/s. pipe with diameter 4 cm is 4 m/s. Calculate the amount of fluid flowing pe Calculate the amount of fluid flowing pe second (Q)second (Q)


If the rate of flow of the water that out from If the rate of flow of the water that out from the pipe as shown in diagram below is 10 the pipe as shown in diagram below is 10 litre/s. Determine the speed of water in the litre/s. Determine the speed of water in the large hole and in the small hole.large hole and in the small hole.

R1= 20 cm R2= 10 cm


An ideal fluid flow through a pipe that has An ideal fluid flow through a pipe that has two difference cross-sectional area. The two difference cross-sectional area. The diameter of both area are 15 cm and 10 diameter of both area are 15 cm and 10 cm. If the fluid’s speed in the smaller area cm. If the fluid’s speed in the smaller area 9 m/s, Determine the speed of the fluid 9 m/s, Determine the speed of the fluid when it pass trhough the large areawhen it pass trhough the large area

Bernoulli’s EquationBernoulli’s Equation

In general form, which In general form, which either speed of the either speed of the flow or the height of flow or the height of fluid change, the fluid change, the Bernoulli’s equation is Bernoulli’s equation is expressed in the form expressed in the form of :of :

2222

121

212

11 ghgvPghgvP


A water pipe having a 2.5 cm inside A water pipe having a 2.5 cm inside diameter carries water into the basement diameter carries water into the basement of a house at a speed og 0.9 m/s and a of a house at a speed og 0.9 m/s and a pressure of 170 kPa. If the pipe tapers to pressure of 170 kPa. If the pipe tapers to 1.2 cm and rises to the second floor 7.6 m 1.2 cm and rises to the second floor 7.6 m above the input point. What are the (a) above the input point. What are the (a) speed and (b) water pressure at the speed and (b) water pressure at the second floor ?second floor ?

Flow from a tank holeFlow from a tank hole

)(2 212 hhgv

The speed of the liquid un the tank The speed of the liquid un the tank (v(v11) is very small compared to the ) is very small compared to the speed of the fluid through the hole speed of the fluid through the hole (v(v22) , thus we assume that v) , thus we assume that v11= 0= 0

The atmospheric pressure at the The atmospheric pressure at the top of tank and at the hole are top of tank and at the hole are same Psame P11= P= P22= P= P00. .

Based on equation of BernoullyBased on equation of Bernoully

ghgh11= ½ = ½ vv2222 – – ghgh22 and :and :


A tank with a large A tank with a large diameter filled with diameter filled with water 3.6 m of depth. water 3.6 m of depth. 2 m above the base 2 m above the base there is a hole. At there is a hole. At what distance x does what distance x does the water stright the the water stright the floor at the first time ?floor at the first time ? x

3.8

2

The venturimeterThe venturimeter

2211

21

21

222

121

222

12

212

11

)(

vAvA

and

ghPP

vvPP

vPvP

The bernoulli’s Equation in this case will be in the form of :

We will get :

1

22

2

1

1

AA

ghv

Or :

2

1

2

2

1

2

AA

ghv

A venturimeter with the big section area 10 A venturimeter with the big section area 10 cmcm22 and small section area 5 cm and small section area 5 cm22 is used is used to measure the velocity of water flow. If the to measure the velocity of water flow. If the height difference of water surface is 15 height difference of water surface is 15 cm. Calculate the velocity of water flow in cm. Calculate the velocity of water flow in the big and small section ! ( g = 10 msthe big and small section ! ( g = 10 ms22))

Venturimeter with manometerVenturimeter with manometer

)(

)'(222

21

21 AA

ghAv

)(

)'(222

21

12 AA

ghAv

Student ActivityStudent Activity Diagram below is a venturimeter with has manometer. The rate of Diagram below is a venturimeter with has manometer. The rate of

flow of water which flow through the venturi is 3,200 cmflow of water which flow through the venturi is 3,200 cm33/s. the cross /s. the cross section area 1 and area 2 each is 40 cmsection area 1 and area 2 each is 40 cm22 and 16 cm and 16 cm22. The density of . The density of mercury 13.6 g/cmmercury 13.6 g/cm33

a. what is the speed of the water at the area 1 and area 2 ?a. what is the speed of the water at the area 1 and area 2 ?b. what is the difference of pressure between pipe 1 and pipe 2b. what is the difference of pressure between pipe 1 and pipe 2c. what is the difference of mercury high at the manometer ?c. what is the difference of mercury high at the manometer ?

Pitot TubePitot Tube

22

1aab vPP

Bernoulli’s principle gives :

Vb = 0

The hydrolic pressure of point c and d are the same, Pc= Pd

ghPP ab 'The combination of two equation above :

gh

va'2


When the air flows When the air flows through a Pitot tube, through a Pitot tube, he difference in hight he difference in hight between mercury between mercury columns in columns in mamometer is 2 cm. mamometer is 2 cm. Determine the flow Determine the flow speed of air (rspeed of air (rairair 1.29 1.29

kg/mkg/m33 and r and rmercurymercury- 13.6 - 13.6

g/cmg/cm33))

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Hydrodynamics

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