A venturi meter is a device placed in a pipeline to allow for the measurement of flow

Question:

A venturi meter is a device placed in a pipeline to allow for the measurement of flow through that pipeline. As shown in the following figure, the meter consists of a tapered reduction of the pipe diameter followed by an expansion back to the original diameter. Pressure taps in the upstream section and the narrow neck (called the "throat") of the meter make it possible to measure the difference between the pressures at those locations. The flow rate can be determined from that pressure difference using methods discussed in this chapter.

Flow pressure tap 1 I (AP pressure tap

As a summer engineer for the Valuchem Chemical Company, you are assigned to provide a way to monitor the flow rate of water (density = 62.4 lb_m/ƒt³) through a 3-in diameter pipe in a process. You have ordered and installed a venturi meter with a throat diameter of 1.2 in. Now you need to relate the measured pressure difference to the flow rate.

a. Use a spreadsheet to predict the performance of the meter. Neglecting friction, have the spreadsheet calculate the pressure difference (ΔP = P₁− P₂) in units of psi for a series of flow rates ranging from 0 to 100 gallons per minute (GPM) in increments of 5 GPM. Display the pipe and throat diameters and the fluid density in separate cells, so that the values can be changed for different designs.
b. Have the spreadsheet plot a calibration curve for the flow meter: plot the flow rate (vertical axis) as a function of the pressure difference (horizontal axis).
c. The pressure indicator on the venturi meter shows a pressure difference of 2.75 psi. Use your graph from (b) to estimate the flow rate of the water. Turn in your derivation of the function(s) you used in the spreadsheet along with the spreadsheet and the graph (show on the graph how you got your answer to (c)).
Solve the problem entirely by hand for one value of DP, including unit conversions (note: as in Example 7.2, you may need to convert between units containing lbm and units containing lbƒ). Then construct your spreadsheet.

EXAMPLE 7.2 (continued) We have performed the calculation suggested by Equation 7.2, but the answer doesn't