Comparing The Volumetric Flow Rate Of The Venturi Effect

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Introduction
Bernoulli principle is a statement of conservation of energy per unit mass for an ideal fluid in steady motion, where it states the sum of pressure, kinetic and potential energies per unit volume is constant (Munson, et al., 2013). Venturi effect is where the pressure of the fluid decreases which causes its velocity to increase as it passes through a constricted section of a pipe. This is the basis of this report’s investigation.
The aim of this investigation is to compare the flow rate obtained from the Venturi meter to the flow rate obtained from a velocity profile measured with a Pitot probe. This aim is achieved by measuring the volumetric flow of air in a pipe using a Venturi and calculating the flow rate from a velocity traverse of a pipe using a Pitot tube. Then comparing the results obtained from both measurements and commenting upon the
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Continuity Principle states the volumetric flow rate is constant as it flows through the Venturi tube (Munson, et al., 2013). This is shown in equation 4. Q=A_1 v_1=A_2 v_2 (4)

v_2=A_1/A_2 v_1 (5)

Where, Q = volumetric flow rate [m3s-1], A = cross-sectional area [m2], and 1 & 2 are two arbitrary points in the flow of fluid.
Substituting v2 from equation 5 in to equation 2 and rearranging this to make v1 the subject, then substituting this into equation 4 derives equation 6, which is used to calculate the volumetric flow rate of fluid across the Venturi tube. Q〖=A〗_1 v_1=A_1 √(2 ((p_1-p_2))/(〖ρ_air [(A_1/A_2 )〗^2-1])) (6)

The p_2-p_1 can be measured from the difference in heights from the U-tube manometer, which is ρg∆h, where ρ is the density of the liquid in the manometer and ∆h is the difference in heights between the manometers. This changes equation 6 to equation 7. 〖Q=A〗_1 v_1=A_1 √(2 ((ρ_water g∆h))/(〖ρ_air [(A_1/A_2 )〗^2-1]))

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