The water depths upstream and downstream of a hydraulic jump is 0.3 m and 1.2 m. Determine flow rate

This question is incomplete, the complete question is;

the water depths upstream and downstream of a hydraulic jump is 0.3 m and 1.2 m. Determine flow rate  ( in m³ ) if the rectangular channel is 20 m wide.

the flow rate is 32.549 m³/sec

Explanation:

Given that

y₁ = 0.3 m

y₂ = 1.2 m

β = 20 m

Now for Rectangular Channel, we know that;

2q²/g = y₁y₂( y₁ + y₂)

where g = 9.81 m/s²

and q = Q/β

so

2(Q/β)²/g = y₁y₂( y₁ + y₂)

we substitute our given values

2(Q/20)²/9.81 = 0.3 × 1.2( 0.3 + 1.2)

2(Q²/400)/9.81 = 0.36(1.5)

2(Q²/400) = 0.54 × 9.81

Q²/400 = 5.2974 / 2

Q²/400 = 2.6587

Q² = 1059.48

Q = √1059.48

Q = 32.549 m³/sec

Therefore the flow rate is 32.549 m³/sec

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