GATE 2022 CE (CE2) – Question 56
A hydraulic jump takes place in a 6 m wide rectangular channel at a point where the upstream depth is 0.5 m (just before the jump). If the discharge in the channel is 30 m3/s and the energy loss in the jump is 1.6 m, then the Froude number computed at the end of the jump is ___________. (round off to two decimal places) (Consider the acceleration due to gravity as 10 m/s2.)
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.20 to 0.22
Explanation
The unit-width discharge is q=30/6=5 m²/s. Upstream specific energy is $E_1=0.5+q^2/[2g(0.5)^2]=5.5$ m. Using the supplied loss gives E₂=3.9 m.
Solve $y_2+25/(20y_2^2)=3.9$ on the subcritical branch: y₂≈3.814 m. Then $Fr_2=q/\sqrt{gy_2^3}\approx0.212$, rounded to **0.21**. However, momentum-conjugate depths predict a different loss; the given data are inconsistent.