Volume Flow Rates in Physics Problems

By Consumer Dummies

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

  1. 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?

  2. 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?

  3. 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?

  4. 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:

  1. 4.0 m/s

    Use the equation of continuity:

    image0.png

    You know that

    image1.png

    and that

    image2.png

    Solve the continuity equation for

    image3.png

  2. 0.25 m

    Use the equation of continuity:

    image4.png

    In terms of the stream width

    image5.png

    and depth d, the cross-sectional area of the stream is

    image6.png

    Use this in the continuity equation:

    image7.png

    You know that

    image8.png

    so you can solve the continuity equation for the width

    image9.png

  3. 5.0

    You know that

    image10.png

    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

    image11.png

    When combined with the previous equation, you get

    image12.png

    You also know that

    image13.png

    Combine these equations to find

    image14.png

  4. image15.png

    Flow rate is the volume of fluid moving past a point per unit time. The volume of fluid that enters the pool is

    image16.png

    The time it takes for this volume of water to enter the pool is

    image17.png

    The volume flow rate is therefore

    image18.png