Question

Determine the critical depth for 50m3/s flowing in a trapezoidal channel with bottom-width 4 m and side slopes of 1.5:1 (H:V). If the depth of flow is 3 m, calculate the Froude number and state weather the flow is subcritical or supercritical.

Answer 1

To determine the critical depth for a flow in a trapezoidal channel, use the specific energy equation and substitute the given values to solve for the critical depth.

Step-by-step explanation:

To determine the critical depth in a trapezoidal channel, we need to use the specific energy equation. The specific energy equation is given by:

E = (V^2 / 2g) + (y - B) * (B + (S * y)) / A

where:

• E is the specific energy
• V is the velocity of flow
• g is the acceleration due to gravity
• y is the depth of flow
• B is the bottom width of the channel
• S is the side slope of the channel
• A is the cross-sectional area of flow

Given that the flow rate is 50 m^3/s, the bottom width is 4 m, the side slopes are 1.5:1, and the depth of flow is 3 m, we can substitute these values into the specific energy equation and solve for the critical depth.

By rearranging the equation and solving for y, we can find the critical depth:

y = (2gQ) / (V^2 + 2gB)

Substituting the given values, we get:

y = (2 * 9.8 * 50) / (3^2 + 2 * 9.8 * 4) = 4.79 m

The critical depth for a flow rate of 50 m^3/s in the trapezoidal channel is approximately 4.79 m.