Question

In a rectangular channel of 12 meters width, water flows at a rate of 150 cubic meters per second. At the end of the channel, there is a horizontal concrete apron of 12 meters width, on which the water depth is 3 meters. Calculate the velocity of the water in the channel.

Answer 1

The velocity of the water in the channel is 4.17 meters per second, calculated using the continuity equation for fluid flow by dividing the given flow rate by the cross-sectional area of the channel.

Step-by-step explanation:

To calculate the velocity of the water flowing in the rectangular channel, we can use the continuity equation for fluid flow, which states that the flow rate must remain constant along the channel. The flow rate is defined as the product of the cross-sectional area of the flow and the velocity of the water:

Flow rate (Q) = Area (A) × Velocity (V)

Given that the water depth at the end of the channel is 3 meters and the width of the channel is 12 meters, the cross-sectional area (A) at the end is:

A = width × depth = 12 m × 3 m = 36 m²

We are told that the flow rate (Q) is 150 cubic meters per second. We can now solve for the velocity (V):

V = Q / A = 150 m³/s / 36 m² = 4.17 m/s

Therefore, the velocity of the water in the channel is 4.17 meters per second.