Bernoulli's Equation: Problem Solving

A Venturi meter is installed in a sewage system to measure the wastewater flow rate. If the flow rate is known and viscous effects are negligible, what is the pressure difference indicated by the pressure gauge attached to the flowmeter?

First, calculate the cross-sectional areas of both the pipe and the throat using their respective diameters.

Then, using the continuity equation, determine the velocities at both sections based on the given flow rate.

Since area and velocity are inversely related, the wastewater will speed up as it moves from the larger-diameter pipe into the smaller throat.

Next, apply Bernoulli's equation, which relates the pressure difference between two points in the flow to the change in velocity.

This equation shows that as the velocity increases when the water moves from the larger pipe to the smaller throat, there will be a corresponding pressure drop.

Finally, calculate the pressure difference between the pipe and the throat by substituting the velocities into Bernoulli's equation.

The pressure gauge attached to the flowmeter will indicate the final pressure difference.