Water is flowing through a PVC pipe at a rate of 800 ft /min The maximum flow of water in a pipe can be modeled by the formula F = Av , where A is the cross- sectional area of the pipe and is the velocity of the water. Find the maximum flow, in f ^ 2 / m * in , of a PVC pipe whose diameter is 4 inchesHint: Convert inches to feet.
the radius of the pipe is 2in, so
F = (4π in^2)(1ft^2/144in^2)(800 ft/min)
or, per the hint,
F = π(1/6 ft)^2(800 ft/min)
To find the maximum flow of a PVC pipe, we need to calculate the cross-sectional area (A) of the pipe first. Given that the diameter of the pipe is 4 inches, we can use the formula for the area of a circle to find A.
The formula for the area of a circle is A = πr^2, where r is the radius of the circle.
First, let's convert the diameter of the pipe from inches to feet:
1 foot = 12 inches
So, 4 inches = 4/12 feet = 1/3 feet
Now, we can calculate the radius of the circle:
radius (r) = 1/2 * diameter
= 1/2 * (1/3) feet
= 1/6 feet
Plugging the radius into the formula for the area of a circle, we have:
A = π * (1/6)^2
= π/36
Next, we are given the velocity of the water, which is 800 ft/min. Let's plug in this value into the formula for the maximum flow (F = Av):
F = A * v
= (π/36) * 800
= 800π/36
Finally, to find the maximum flow in f^2/m*in, we need to convert the units.
1 square foot (ft^2) = 0.092903 square meters (m^2)
1 inch (in) = 0.0254 meters (m)
Converting the units, we have:
F = (800π/36) * (0.092903) * (0.0254)
≈ 7.63 π f^2/m*in
Therefore, the maximum flow of a PVC pipe with a diameter of 4 inches is approximately 7.63 π f^2/m*in.