Using physics, you can determine how the flow rate of a liquid is affected by cross-sectional area. For example, using the equation of continuity, given the flow rate and cross-sectional area of the opening to a water hose, you can calculate the speed at which the water exits the hose.
Here are some practice questions that you can try.
Practice questions
Water travels through a hose at 0.8 meters per second. If the cross-sectional area of the exit nozzle is one-fifth that of the hose, at what speed does water exit the hose?
You are watching leaves float past you in a stream that is 0.76 meters wide. At one point, you estimate that the speed of the leaves triples. If the stream has a constant depth, what is the width of the stream at this point?
The volume flow rate through pipe 1 is 2.5 times that of pipe 2. If the cross-sectional area of pipe 1 is one-half that of pipe 2, what is the ratio of the flow speed in pipe 1 to that in pipe 2?
If the water that exits a pipe fills a pool that is 3 meters deep, 20 meters long, and 5 meters wide in 3 days, what is the flow rate?
Answers
The following are the answers to the practice questions:
4.0 m/s
Use the equation of continuity:
You know that
and that
Solve the continuity equation for
0.25 m
Use the equation of continuity:
In terms of the stream width
and depth d, the cross-sectional area of the stream is
Use this in the continuity equation:
You know that
so you can solve the continuity equation for the width
5.0
You know that
are the volume flow rate through pipes 1 and 2, respectively. In terms of cross-sectional area and flow speed, the volume flow rate is
When combined with the previous equation, you get
You also know that
Combine these equations to find
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Flow rate is the volume of fluid moving past a point per unit time. The volume of fluid that enters the pool is
The time it takes for this volume of water to enter the pool is
The volume flow rate is therefore
