Answer:
2.8 cm/s
Explanation:
The flow speed in a tube or pipe is equal to the volumetric flow rate divided by the cross sectional area. The volumetric flow rate can be found by dividing the volume of the tank by the time it takes to process all the water, and the cross sectional area of a round tube is pi times the square of the radius. The volume of a rectangular tank is equal to the width times the length times the height.
The required equations are:
v = Q / A
where v is flow speed, Q is flow rate, and A is cross sectional area.
Q = V / t
where V is the volume of the tank and t is time.
A = πr²
where r is the radius of the tube, or half the diameter.
V = WLH
where W is the width, L is the length, H is the height.
First, find the volume of the tank using the dimensions of the tank. Make sure to convert all units to the same unit of measure. In this case, we'll convert meters to centimeters.
V = WLH
V = (36 cm) (100 cm) (60 cm)
V = 216,000 cm³
Next, use the volume and the time to find the flow rate. Convert hours to seconds.
Q = V / t
Q = 216,000 cm³ / (3 h × 3600 s/h)
Q = 216,000 cm³ / (10,800 s)
Q = 20 cm³/s
Now find the cross sectional area of the tube using the radius.
A = πr²
A = π (3.0 cm / 2)²
A = 7.07 cm²
Finally, use the flow rate and the area to find the flow speed.
v = Q / A
v = (20 cm³/s) / (7.07 cm²)
v = 2.8 cm/s
The flow speed through the tube is approximately 2.8 cm/s.
