Water flowing through a 2.8 cm-diameter pipe can fill a 200 L bathtub in 5.8 min.What is the speed of the water in the pipe?

Answer 1

To find the speed of the water in the pipe, we first need to determine the volume flow rate, which is the volume of water that flows through the pipe per unit of time. We know that a 200 L bathtub can be filled in 5.8 min, so the volume flow rate is:

Volume flow rate = Volume / Time
Volume flow rate = 200 L / 5.8 min

We need to convert the units to be consistent, so we'll convert the volume to cubic meters (m^3) and the time to seconds (s):

1 L = 0.001 m^3
200 L = 200 * 0.001 m^3 = 0.2 m^3

1 min = 60 s
5.8 min = 5.8 * 60 s = 348 s

Now we can find the volume flow rate:

Volume flow rate = 0.2 m^3 / 348 s ≈ 0.000574713 m^3/s

Next, we need to find the cross-sectional area of the pipe. The diameter of the pipe is 2.8 cm, so the radius is half of that, 1.4 cm. We need to convert the radius to meters:

1.4 cm = 1.4 * 0.01 m = 0.014 m

Now we can find the cross-sectional area of the pipe, A, using the formula for the area of a circle:

A = πr^2
A = π(0.014 m)^2 ≈ 0.000615752 m^2

Finally, we can find the speed of the water, v, using the formula:

v = Volume flow rate / Cross-sectional area
v = 0.000574713 m^3/s / 0.000615752 m^2 ≈ 0.933389 m/s

The speed of the water in the pipe is approximately 0.93 m/s.