The GATE Grind

GATE 2025 CE (CE1) – Question 19

Hydraulics · Dimensional analysis and hydraulic similitude · 1 mark · Multiple choice

For a flowing fluid, a dimensionless combination of velocity ($V$), length scale ($l$), and acceleration due to gravity ($g$) would be

  1. $\frac{V^2}{gl}$
  2. $\frac{Vg}{l}$
  3. $\frac{gl^2}{V}$
  4. $\frac{l}{V^2g}$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $\frac{V^2}{gl}$

Explanation

The dimensions are $V = LT^{-1}$, $l = L$ and $g = LT^{-2}$. Then $\frac{V^2}{gl} = \frac{L^2T^{-2}}{L \cdot T^{-2} \cdot L} = 1$, so it is dimensionless. This is the square of the Froude number. The other combinations keep a length or a time.