Water flows at the rate of 12 m3/s in a 6 m wide rectangular channel. ...
Assuming channle bed to be horizontal and frictionless.
q = 12/6 = 2m
3/s/m
Initial Froude No.
From Belenger’s Momentum equation for a rectangular channel
= 5.018
∴ Y
2 = 5.018 × 0.3 = 1.505 m
Head loss in the jump (h
L) =
= 0.968 m
Power lost in the jump = γ
wQh
L= (9.81 × 12 × 0.968) kW
= 114.04 kW
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Water flows at the rate of 12 m3/s in a 6 m wide rectangular channel. ...
Given information:
- Flow rate of water, Q = 12 m^3/s
- Width of the rectangular channel, B = 6 m
- Upstream depth before the hydraulic jump, h1 = 30 cm = 0.3 m
- Acceleration due to gravity, g = 9.81 m/s^2
- Density of water, ρ = 1000 kg/m^3
To find: Energy loss in the hydraulic jump
1. Determine the upstream velocity:
- The cross-sectional area of flow, A1 = B * h1
- The upstream velocity, V1 = Q / A1
2. Determine the downstream depth:
- The downstream depth after the hydraulic jump, h2 = 4 * h1
3. Determine the downstream velocity:
- The cross-sectional area of flow, A2 = B * h2
- The downstream velocity, V2 = Q / A2
4. Calculate the energy head before the hydraulic jump:
- The energy head before the jump, H1 = (V1^2) / (2g) + (h1)
5. Calculate the energy head after the hydraulic jump:
- The energy head after the jump, H2 = (V2^2) / (2g) + (h2)
6. Calculate the energy loss during the hydraulic jump:
- The energy loss, H_loss = H1 - H2
7. Convert the energy loss to kilowatts:
- Power = H_loss * Q * g * ρ / 1000
Detailed Calculation:
1. Upstream velocity:
- A1 = B * h1 = 6 m * 0.3 m = 1.8 m^2
- V1 = Q / A1 = 12 m^3/s / 1.8 m^2 = 6.67 m/s
2. Downstream depth:
- h2 = 4 * h1 = 4 * 0.3 m = 1.2 m
3. Downstream velocity:
- A2 = B * h2 = 6 m * 1.2 m = 7.2 m^2
- V2 = Q / A2 = 12 m^3/s / 7.2 m^2 = 1.67 m/s
4. Energy head before the hydraulic jump:
- H1 = (V1^2) / (2g) + (h1) = (6.67 m/s)^2 / (2 * 9.81 m/s^2) + 0.3 m = 2.84 m
5. Energy head after the hydraulic jump:
- H2 = (V2^2) / (2g) + (h2) = (1.67 m/s)^2 / (2 * 9.81 m/s^2) + 1.2 m = 1.33 m
6. Energy loss during the hydraulic jump:
- H_loss = H1 - H2 = 2.84 m - 1.33 m = 1.51 m
7. Energy loss in kilowatts:
- Power = H_loss * Q * g * ρ / 1000 = 1.51 m * 12 m^3/s * 9.81 m/s^2 * 100