1. SUB:-FLUID MECHANICS TOPIC:-FLOW MEASUREMENT DEVICES SUBMITTED TO: KULDEEP SIR Government engineering college, valsad

2. Prepare by:- group 6 NameEnrollment no. AHIR NIRMAL130190106001 MALAVI GAUTAM130190106024 PANCHAL GAURANG130190106027 PATEL YASH130190106044

3. TOPICS:- Measurement of discharge-venturimeter Orificemeter Nozzle meter Rotameter Measurement of velocity- pitot tube Orifice classification Flow through reservoir opening i.e. orifice,trajectory of free jet Hydraulic coefficients Experimental determination of hydraulic coefficient Small and large orifice Time of emptying a tank with orifice Mouthpieace-classification External cylindrical mouthpiece

4. Convergent-divergent mouthpiece Borda’s mouthpiece Notches and weirs-discharge over rectangular notch and triangular notch Velocity of approach End contractions Cippoletti notch Time of emptying a tank with notch or weir Ventilation of weir Sutro weir

5. Measurement of discharge-Venturimeter The Venturimeter was invented by Clements Hershel in 1887 and has been named in the honour of an Italian engineer Venturi. It is a device used for measuring the rate of a flow of a fluid flowing though a pipe. It consists of three parts. (i)=A short converging part, (ii)=Throat & (iii)=Diverging part. The working principle of Venturimeter is based on Bernoulli’s equation.

6. Venturimeter Consider a Venturimeter fitted in a horizontal pipe through Which a fluid is flowing. Let d 1 = diameter at inlet or at section 1, p 1 = pressure at section 1, V 1 = velocity of fluid at section 1, a 1 = area of at section 1, & d 2, p 2, V 2 and a 2 are the corresponding values at section 2. Applying Bernoulli’s eq. at section (1) & (2), we get

7. Venturimeter

8. Since pipe is horizontal, z 1 =z 2 But Difference of pressure heads at section (1) & (2) …eq.(1) Applying continuity eq. at section (1) & (2), we have, or

9. Venturimeter Substituting this value of V 1 in eq. (1)

10. Venturimeter · ̇ · Discharge, Q = …eq.(2) Eq.(2) gives the discharge under ideal conditions & is known as theoretical discharge. Actual discharge is …eq.(3) where C d = Co-efficient of discharge of Venturimeter It varies between 0.96 to 0.98.

11. Orificemeter Pipe orifice is a device used for measuring the rate of floe of a fluid through a pipe. It is also called orifice meter and orifice plate. The orifice meter consists of a thin, circular plate with a hole in it. The plate is held in the pipeline between two flanges. Pipe orifice is a cheaper device as compared to venturimeter. It also works on the same principle as that of venturimeter. The orifice diameter is kept generally 0.5 times the diameter of the pipe, though it may vary form 0.4 to 0.8 times the pipe diameter. A differential manometer is connected at section (1) which is at a distance of 1.5 to 2 times the pipe diameter upstream from the orifice plate, and at section

12. Orificemeter

13. (2) which is at a distance of about half the diameter of the orifice form the orifice plate on the downstream side. p 1 = pressure at section 1, V 1 = velocity of fluid at section 1, a 1 = area of at section 1, & d 2, p 2, V 2 and a 2 are the corresponding values at section 2. Applying Bernoulli’s eq. at section (1) & (2), we get

14. Orificemeter …eq.(4) Now section (2) is at the vena contracta & a 2 represents the area at the vena contracta. If a 0 is the area of orifice then, we have Coefficient of contraction, Applying continuity eq. at section (1) & (2), we have, or

15. Orificemeter Substituting this value of V 1 in eq. (4), we get · ̇ · The discharge,Q = …eq.(5)

16. Orificemeter The above expression is simplified by using

17. Orificemeter Substituting the value of C c iv eq.(5), we get …eq.(6) Where C d is co-efficient of discharge for Orifice meter.

18. Nozzle meter In the flow nozzle the diverging cone of the venturimeter is omitted. The flow nozzle is thus a truncated form of the venturimeter. It is simpler than the venturimeter & can be installed between the flanges of a pipe line. The flow nozzle provides smooth rounded entrance which practically eliminates the vena contracta. It serves same purpose as the venturimeter. The non recoverable loss is large because there is no diffuser provided for gradual expansion. The discharge other equations for the flow nozzle are the venturimeter and can be derived in the same manner.

19. Nozzle meter Fig.

20. Rotameter A rotameter is discharge measuring device. The rotameter is a variable area meter installed in a vertical segment of a pipeline. A rotameter consists of an accurately ground glass tube diver- ging upwards & flow made of a denser material than the fluid flowing through the tube. The free area between float and inside wall of the tube forms an annular orifice. The tube is mounted vertically with the small end at the bottom. Where there is no flow through rotameter, the float rests at the metering tube where the maximum diameter of the float is approximately the same as the bore of the tube. When fluid enters the metering tube tube, the float moves up, and the flow

21. Rotameter area of the annular orifice increases. The pressure differential across the annular orifice is proportional to square of its flow area & the square of the rate. The float is pushed upward until the lifting force produced by the pressure differential across its upper & lower surface is equal to the weight of the float. If the flow then rises, widening the annular orifice until the force caused by the pressure differential is again equal to the weight of the float. Thus, the pressure differential remains constant & the free area between float & inside wall of the flow rate. Every float position corresponds to one particular flow rate for a fluid of a given density & density and viscosity. A calibration scale

22. Rotometer printed on the tube or near it, provides a direct indication of flow rate. A rotameter is generally used in chemical industries where high degree of accuracy is not required and the flow varies within a limited range.

23. Rotometer

24. Pitot tube The pitot tube isused to measure the velocity of a fluid stream & consists of a simple L shaped tube facing into incoming flow. It is based on the principle that if the velocity of flow at a point becomes zero, pressure head is increased dur to the conversion of the kinetic energy into pressure energy. The velocity of flow is determine by measuring the rise of fluid in a tube. Consider two point (1) & (2) at the same level in such a way that point(2) is just as inlet of the pitot tube & point(1) is far away from the tube.

25. Pitot tube

26. Let p 1 = pressure at point (1), V 1 = velocity of flow at point (1), p 2, V 2 are the corresponding to point (2), H = depth of tube in the liquid, h = rise of liquid in the tube above the free surface. Applying Bernoulli’s eq. Since z 1 = z 2,and final velocity, V 2 = 0 =pressure head at(1)=H = pressure head at(2)=h+H

27. Pitot tube Substituting these values, we get or This is theoretical velocity. Actual velocity is given by Where C v = Co-efficient of pitot tube Hence, velocity at any point, …eq.(7)

28. Pitot tube When the pitot tube is used in a channel, the value of h can be Directly as shown in fig. but, If it is used in a pipe,the difference between the static pressure & total pressure must be measured with a differential U-tube manometer, using a static pressure tapping in the pitoti-static tube, inner tube is used to measure total pressure while the outer tube has holes in its surfaces to measure the static pressure. Note :- The difference between total pressure & static pressure is called dynamic pressure.

29. Pitot tube Value of ‘h’ by differential u-tube manometer Case 1:- Differential manometer containing a liquid flowing through the pipe. Let, s h = Sp.gravity of heavier liquid in U-tube s 0 =Sp.gravity of fluid through pipe x = Difference of the heavier liquid columns in U-tube.

30. Pitot tube Case 2:- Differential manometer containing a liquid than the liquid lighter than the liquid flowing through the pipe. Let, s l = Sp.gravity of lighter liquid in U-tube s 0 =Sp.gravity of fluid through pipe x = Difference of the lighter liquid columns in U-tube. Then,