Question

water, of density 1000 kg/m3 , is flowing in a drainage channel of rectangular cross-section. the width of the channel is 12 m, the depth of the water is 4.0 m and the speed of the flow is 3.2 m/s. at what rate is water flowing in this channel? give your answer in m3 /s but do not include the units in the answer box.

Answer 1

The flow rate of water through the channel is found by multiplying the cross-sectional area (48 m²) by the velocity (3.2 m/s), resulting in a flow rate of 153.6 m³/s.

Step-by-step explanation:

The student is asking about the rate at which water is flowing through a channel. To find this, we use the formula for volumetric flow rate, which is the product of the cross-sectional area and the velocity of the fluid.

The cross-sectional area of the channel is found by multiplying the width of the channel (12 m) by the depth of the water (4.0 m).

Therefore, the area A is 12 m × 4.0 m = 48 m².

Then we multiply the area by the velocity of the water (3.2 m/s) to find the flow rate Q.

Q = A × v = 48 m² × 3.2 m/s = 153.6 m³/s