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Questions on Venturi Meter for Measuring Fluid Flow Rates

Question

A Venturi meter is a device used to measure fluid flow rates. It consists of a tapered constriction in a line with pressure taps leading to a differential manometer at points upstream of the constriction and at the point of maximum constriction. The manometer reading is directly related to the flow rate in the line. 

a) Starting from the energy balance on an open system at steady state, derive Bernoulli’s equation:

ΔP⁄ρ + Δv2/2 + gΔz = 0

where ∆ = value at point 2 – value at point 1, P is the pressure of the fluid, ρ is the fluid density, v is the average fluid velocity, g is gravitational acceleration, and z is average fluid height.  Bernoulli’s equation is an expression for the conservation of mechanical energy where the process is assumed to be frictionless with no shaft work. The following relationships may be helpful to you:

v = 1/ρ

ΔU - Q/m = F

where V is the specific volume of the fluid [volume/mass], U is the specific internal energy [energy/mass], Q is the heat flow rate [energy/time], m is the mass flowrate, and F is defined as the energy lost to friction in pipes.  

b) Suppose the flow rate of an incompressible fluid is to be measured in a Venturi meter when A, the cross-sectional area at point 1, is four times that at point 2. Relate the velocities v11 and v at points 1 and 2, respectively.

c) Using your results from parts a) and b), relate the pressures in point 1 and point 2 (P2 and P, respectively).

d) Suppose this meter is used to measure the flowrate of a stream of water, using mercury as 2 the manometer fluid. A manometer reading of h = 38 cm is recorded. What is the volumetric flow rate of water if the pipe diameter at point 1 is 15 cm? If carbon tetrachloride were instead used as the manometer fluid, what would the manometer read?


Summary

The question belongs to Chemical Engineering and the question is about Venturi meter used for measuring fluid flow rates. If the flow rate of an incompressible fluid is to be measured in a Venturi meter, what would be the result. This and other questions have been answered with calculations in the solution.

Note: The answers are in handwritten format

 

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