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Delhi

Fluid Mechanics

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Published in: Mechanical
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Application of Bernoulli Equation.

Navin S / Hyderabad

6 years of teaching experience

Qualification: B.Tech/B.E. (Bit Sindri , Sindri - 2011)

Teaches: Algebra, Geography, Mathematics, Physics, All Subjects, Biology, Science, Chemistry, Bank PO, PSU Exam, SBI Exam, AIEEE, BITSAT, Drawing, Mechanical, Production

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  1. Lecture 11 : Practical applications of Bernoulli's equation Objective: To study the applications of the Bernoulli's equation Venturimeter Orifice meter Pitot-tube
  2. Venturimeter Venturimeter: is a device used for measuring the rate of flow of a fluid flowing through a pipe. It consists of three parts: • A short converging part Throat • Diverging part Throat Inlet 2 1 x
  3. Let dl = diameter at the inlet (section 1) = pressure at section 1 VI = velocity at section 1 area at section 1 d2, P2, 1/2, A2 are the corresponding values at the throat (section 2) Applying Bernoulli's equations at sections 1 and 2, we get 2 PI W 2 Pg 2g Pg 2g As pipe is horizontal Zl=Z2 2 PI — P 2 _ v2 2 2g 2 2 2g
  4. PI P2 difference of pressure heads at sections 1 and 2. Where h = Pg From the continuity equation at sections 1 and 2, we obtain Hence Discharge Al VI = A2V2 VI = 1222 Al 2 — 1422 2gh Q = = A2h 2gh — 1422 Note that the above expression is for ideal condition and is known as theoretical discharge.
  5. Actual discharge will be less than theoretical discharge. 2gh actual Al 2 — 1422 Cd is the coefficient of venturimeter and its value is always less then 1. Expression of 'h' given by differential U-tube manometer: Case 1: The liquid in the manometer is heavier than the liquid flowing through the pipe Sh: Specific gravity of the heavier liquid. So: Specific gravity of the flowing liquid. Case 2: The liquid in the manometer is lighter than the liquid flowing through the pipe h = x 1——L So SL: Specific gravity of the lighter liquid. X: difference of the liquid columns in U-tube
  6. Orifice meter • Orifice meter: is a device used for measuring the rate of flow of a fluid flowing through a pipe. • It is a cheaper device as compared to venturimeter. This also work on the same principle as that of venturimeter. • It consists of flat circular plate which has a circular hole, in concentric with the pipe. This is called orifice. • The diameter of orifice is generally 0.5 times the diameter of the pipe (D), although it may vary from 0.4 to 0.8 times the pipe diameter. 2D 1 Direction of flow Orifice 2 x Vena contracta Differential manometer
  7. Let dl = diameter at section 1 = pressure at section 1 VI = velocity at section 1 area at section 1 d2, P2, v2, & are the corresponding values at section 2. Applying Bernoulli's equations at sections 1 and 2, we get pg 2g Pg 2g 2gh + VI where h is the differential head.
  8. Let Aois the area of the orifice. Coefficient of contraction, cc By continuity equation, we have Hence, Al VI = 142 V 2 Aocc A02c:v; 2gh -k 2gh 2
  9. Thus, discharge, 2gh = 122140 cc If Cd is the co-efficient of discharge for orifice meter, which is defined as
  10. Hence, 2gh — 1402 The coefficient of discharge of the orifice meter is much smaller than that of a venturimeter.
  11. Pitot-tube Orifice meter: is a device used for measuring the velocity of flow at any point in a pipe or a channel. • Principle: If the velocity at any point decreases, the pressure at that point increases due to the conservation of the kinetic energy into pressure energy. • In simplest form, the pitot tube consists of a glass tube, bent at right angles. Let PI = pressure at section 1 = pressure at section 2 VI = velocity at section 1 = velocity at section 2 = 0 H = depth of tube in the liquid h = rise of liquid in the tube above the free surface h H 1 2 Point 2 is just at the inlet of the Pitot-tube Point 1 is far away from the tube
  12. Applying Bernoulli's equations at sections 1 and 2, we get 2 2 But 2gh = z2 , and v2 pg 2g Pg 2g Pressure head at 1=H Pg Pressure head at 2=h+H Pg Substituting these values, we get 2 2g VI = This is theoretical velocity. Actual velocity is given by )act 2gh C = coefficient of pitot-tube

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