Hydrodynamics l l Hydrodynamics is a branch of

Hydrodynamics

l l Hydrodynamics is a branch of physics that studies about the motion of fluid. Ideal Fluid has properties : incompresible and its flow in either steady or laminer. Incompresible means that the density of the fluid does not depend on the pressure, it can not be compressed. A steady flow means that the particle’s motion follows a same flow line.

The Equation of Continuity l l l Volume flow rate (Q) is defined as the amount (volume) of fluid flow per time unit Q = V/t For incompresible fluid, the volume flow rate is the same at any point in the fluid A 1 v 1 = A 2 v 2 or Q 1 = Q 2 Equation above is called continuity equation which states that : at any points in fluid, the rate of volume flow is constant. The speed of flow will be greater if it passes the smaller cross-sectional

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

Student Activity l If the rate of flow of the water that out from the pipe as shown in diagram below is 10 litre/s. Determine the speed of water in the large hole and in the small hole. R 1= 20 cm R 2= 10 cm

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

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

Student Activity l A water pipe having a 2. 5 cm inside diameter carries water into the basement of a house at a speed og 0. 9 m/s and a pressure of 170 k. Pa. If the pipe tapers to 1. 2 cm and rises to the second floor 7. 6 m above the input point. What are the (a) speed and (b) water pressure at the second floor ?

Flow from a tank hole l l l The speed of the liquid un the tank (v 1) is very small compared to the speed of the fluid through the hole (v 2) , thus we assume that v 1= 0 The atmospheric pressure at the top of tank and at the hole are same P 1= P 2= P 0. Based on equation of Bernoully rgh 1= ½ rv 22 – rgh 2 and :

Student Activity l A tank with a large diameter filled with water 3. 6 m of depth. 2 m above the base there is a hole. At what distance x does the water stright the floor at the first time ? 3. 8 2 x

The venturimeter We will get : The bernoulli’s Equation in this case will be in the form of : Or :

l A venturimeter with the big section area 10 cm 2 and small section area 5 cm 2 is used to measure the velocity of water flow. If the height difference of water surface is 15 cm. Calculate the velocity of water flow in the big and small section ! ( g = 10 ms 2)

Venturimeter with manometer

Student Activity l Diagram below is a venturimeter with has manometer. The rate of flow of water which flow through the venturi is 3, 200 cm 3/s. the cross section area 1 and area 2 each is 40 cm 2 and 16 cm 2. The density of mercury 13. 6 g/cm 3 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 2 c. what is the difference of mercury high at the manometer ?

Pitot Tube Bernoulli’s principle gives : Vb = 0 The hydrolic pressure of point c and d are the same, Pc= Pd The combination of two equation above :

Student Activity l When the air flows through a Pitot tube, he difference in hight between mercury columns in mamometer is 2 cm. Determine the flow speed of air (rair 1. 29 kg/m 3 and rmercury 13. 6 g/cm 3)

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