Water flows through a pipe with the inner diameter of 20cm at a speed of 1m/s. How long does it take for the water flowing out from the pipe to fill a cylindrical tank with the base radius of 0.8m and the height of 0.5m?
(pi * .8^2 * .5 m^3)
----------------------- = 32 s
(pi * .1^2 * 1 m^3/s)
To determine the time it takes for the water flowing out from the pipe to fill the cylindrical tank, we need to calculate the volume of water that flows out per second.
First, let's calculate the cross-sectional area of the pipe:
The inner diameter of the pipe is given as 20 cm, which is equivalent to 0.2 m (since 1 m = 100 cm).
The radius of the pipe (r) can be calculated by dividing the diameter by 2:
r = 0.2 m / 2 = 0.1 m
The cross-sectional area of the pipe (A) can be calculated using the formula for the area of a circle:
A = π * r^2
A = π * (0.1 m)^2
A = 0.01π m^2
The speed of the water flowing through the pipe is given as 1 m/s.
Now, let's calculate the volume of water flowing out per second:
The volume of water (V) flowing out per second can be calculated using the formula:
V = A * v
where A is the cross-sectional area of the pipe and v is the speed of water flow.
V = 0.01π m^2 * 1 m/s
V = 0.01π m^3/s
Next, let's calculate the volume of the cylindrical tank:
The base radius of the cylindrical tank is given as 0.8 m, and the height is given as 0.5 m.
The volume of the cylindrical tank (Vtank) can be calculated using the formula:
Vtank = π * r^2 * h
where r is the base radius of the tank and h is the height of the tank.
Vtank = π * (0.8 m)^2 * 0.5 m
Vtank = 1.008π m^3
Finally, let's calculate the time it takes to fill the cylindrical tank:
The time (t) can be calculated using the formula:
t = Vtank / V
where Vtank is the volume of the tank and V is the volume of water flowing out per second.
t = (1.008π m^3) / (0.01π m^3/s)
t = 100.8 s
Therefore, it would take approximately 100.8 seconds for the water flowing out from the pipe to fill the cylindrical tank.