Question

A horizontal venturi flow meter consists of a converging–diverging conduit as indicated in Fig. P5.93. The diameters of cross sections (1) and (2) are 6 and 4 in. The velocity and static pressure are uniformly distributed at cross sections (1) and (2). Determine the volume flowrate (ft^3/s) through the meter if P1 − P2 = 3 psi, the flowing fluid is oil (rho = 56 lbm/ft^3), and the loss per unit mass from (1) to (2) is negligibly small.

Answer 1

To find the volume flow rate through a horizontal venturi flow meter for oil with known diameters and pressure difference, one must use Bernoulli's principle and continuity equation to first calculate the velocities at two cross-sections and then the flow rate.

Step-by-step explanation:

The question involves calculating the volume flow rate in a horizontal venturi flow meter when the pressure difference between two cross-sections is given. The flow meter works on Bernoulli's principle, which relates the velocity of a fluid to its static pressure and density. According to the principle, when fluid flow is incompressible and there is negligible energy loss, the volume flow rate can be derived knowing the pressure difference, the fluid density, and the diameters of the meter's cross sections.

Step-by-step Solution

1. First, we convert the pressure difference from psi to lbft-2 knowing that 1 psi is equal to 144 lbft-2.
2. Calculate the area for both cross-sections using the formula A = πd2/4, where d is the diameter.
3. Apply the continuity equation A1V1 = A2V2 to relate velocities at both cross sections since the mass flow rate must be conserved.
4. Apply Bernoulli's equation P1 + ½ρV12 = P2 + ½ρV22 to find the velocity at cross section (2) using the given pressure difference.
5. Finally, use the continuity equation to find V1 and then the volume flow rate Q = A1V1.