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Hydrodynamics

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**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.

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**The Equation of Continuity**

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 A1v1 = A2v2 or Q1 = Q2 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

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Student Activity 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)

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Student Activity 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. R1= 20 cm R2= 10 cm

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Student Activity 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

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Bernoulli’s Equation 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 :

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Student Activity 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 kPa. 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 ?

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Flow from a tank hole The speed of the liquid un the tank (v1) is very small compared to the speed of the fluid through the hole (v2) , thus we assume that v1= 0 The atmospheric pressure at the top of tank and at the hole are same P1= P2= P0. Based on equation of Bernoully rgh1= ½ rv22 – rgh2 and :

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Student Activity 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

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**The venturimeter Or : We will get :**

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

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A venturimeter with the big section area 10 cm2 and small section area 5 cm2 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 ms2)

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**Venturimeter with manometer**

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Student Activity Diagram below is a venturimeter with has manometer. The rate of flow of water which flow through the venturi is 3,200 cm3/s. the cross section area 1 and area 2 each is 40 cm2 and 16 cm2. The density of mercury 13.6 g/cm3 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 ?

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**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 :

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Student Activity 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/m3 and rmercury g/cm3)

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Prinsip Kerja : Pesawat Terbang

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Thank’s

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