The GATE Grind

GATE 2024 ES – Question 47

Water Resources and Environmental Hydraulics · Environmental Hydraulics · 2 marks · Multiple select

A 3 m×2 m tunnel flows full at 1 m/s with head loss1 m/km. Use g=10 m/s². Which statements are correct?

  1. Hydraulic radius.6 m
  2. Darcy friction factor.048
  3. Hydraulic radius2 m
  4. Darcy friction factor.024

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) Hydraulic radius.6 m; (B) Darcy friction factor.048

Explanation

Area is 6 m² and full wetted perimeter is 10 m, so $R_h=A/P=.6$ m. Hydraulic diameter is $D_h=4R_h=2.4$ m. Darcy–Weisbach gives $h_f/L=fv^2/(2gD_h)$,so $f=.001(2)(10)(2.4)=.048$. Select **A, B**. The enclosed top surface counts in the wetted perimeter.

More Environmental Hydraulics questions

All Environmental Hydraulics questions →