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?
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To find the speed of the water in the pipe, we need to determine the volume flow rate, which is the amount of water that passes through the pipe per unit of time.
First, let's convert the diameter of the pipe from centimeters (cm) to meters (m). Since 1 meter = 100 centimeters, the diameter in meters is 2.8 cm / 100 = 0.028 meters.
The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height. In this case, the height refers to the length of the pipe.
Since we are interested in the flow rate per unit of time, we can rearrange the formula as V/t = A*v, where V/t is the volume flow rate, A is the cross-sectional area of the pipe, and v is the speed of the water.
The radius of the pipe is half of the diameter, so r = 0.028 / 2 = 0.014 meters.
The cross-sectional area of the pipe can be calculated using the formula A = πr^2. Plugging in the values, we get A = π * (0.014)^2 ≈ 0.0006157 square meters.
Now, we can use the volume flow rate formula to find the speed of the water. The volume flow rate is given as 200 L / 5.8 min. To convert this to cubic meters per second (m^3/s), we divide by both 1000 (to convert 1 liter to 1 cubic meter) and 60 (to convert minutes to seconds). So,
Volume flow rate = (200 L / 5.8 min) / (1000 L/m^3) / (60 s/min) ≈ 0.057 m^3/s.
Finally, we can substitute the volume flow rate and the cross-sectional area into the formula V/t = A*v, and solve for v:
0.057 m^3/s = 0.0006157 m^2 * v
v ≈ 92.66 m/s
Therefore, the speed of the water in the pipe is approximately 92.66 meters per second.