Student Activity Packet

"Weir Dam, for Measurement of Water," The Construction of Mill Dams James Leffel & Co., 1874.

Description

In this activity, you will read the student essay entitled "Water Power," locate a small stream, and measure the water's depth and speed. Following the directions given in a handout, you will then be able to calculate the water flow.

Gauging the Waters

When deciding where a mill should be located, a millwright had to know the river's potential power, which meant computing the flow of the river and measuring the available head (vertical drop) at the site. If there is a stream or creek near your school, you can measure the flow in it. To do this, you must measure the speed and cross section of the stream. The problem with measuring the speed is that it varies from the top to the bottom of the stream because the bottom water is dragging over the mud, sand, or rocks. The best way to approximate the average current speed is to take a bottle, fill it most of the way with water so that it floats submerged to the neck, and then time it as it floats down a measured length (say, thirty feet) near the center of the current. If you repeat the measurement about ten times and average the results you will have a reasonable answer for the stream's speed.

Now you need to calculate the cross section. For this you will measure the width of the stream and then measure the depth in about ten places across the river. (If you can walk across the stream, do this with a tape measure. If it's too deep, you can do this from a boat, by dropping a weight on a string and measuring the length of the string.) Calculate the average depth by adding all of the measurements and then dividing by the total number of measurements. You can then multiply by the stream's width to get a cross section in square feet (area = avg. depth x width). The cross section multiplied by the speed of the stream will give you the flow in cubic feet of water per second.

Students on a boat taking stream depth measurements Photos courtesy of Blackstone Valley Tourism Council, Pawtucket, RI.

If the stream drops an appreciable amount and you measure that, you can calculate the power available by using the formula

where Q is the flow rate in cubic feet per second and h is the head in feet. The amount of power in a small stream is quite surprising.

Example

Width of stream = 6.5 feet

Depth measurements (in feet) = .67, 1.25, 1.75, 1.75, 2.5, 2.33, 1.5, 1.5., .75

Average depth = 1.55 feet

Time measurements (in seconds per 30 feet, for example) = 6.5, 5.9, 5.9, 5.7, 5.8, 6.2, 6.1, 5.7, 6.1, 6.0

Average time = 6.0 secs/30 ft, or 1 second for 5 feet, which is the same as a speed of 5 ft/sec.

The cross section is 6.5 ft x 1.55 ft = 10.075 10 sq ft.

The flow is 10 sq ft x 5 ft/sec = 50 cu ft/sec.

If this stream drops 2 feet, then:

So this stream could light 80 100-watt lightbulbs.

One thing you miss with the above calculation is that the water on the top of the stream moves faster than the water on the bottom. As early as the 19th century, millwrights understood this problem. Zachariah Allen explained in his book The Science of Mechanics (1829) how an engineer might measure stream flow more accurately.

"He takes the velocity of the surface of the middle of the stream, by floating a small piece of cork down it. From this experiment he calculates the retarded velocity of the bottom of the stream, and finds the medium velocity by following the following Rule. The velocity of the substance floating on the surface of the middle of the stream is taken in inches per second. From the square root of the number of inches per second he deducts unity, or 1, and then squares the remainder, which gives the velocity at the bottom, and he finds the mean velocity by taking the medium [average] between these two sums."

However you measure the flow, you can see that even small streams have lots of power. No wonder people invented ways to use water power to run their machines! One final question to think about: would the stream whose flow you measured be a good one for building a water-powered mill on?