Q.27 If the actual velocity of jet at the vena contracta in an orifice meter is 'V', the depth of the centre of orifice below the free surface is 'h' and 'g' is the gravitational acceleration, then the coefficient of velocity 'Cv' is:
- A4V / (2gh)3/2
- BV / (2gh)1/2Correct
- C2Vgh / 300
- D2gh / (V)1/2
Solution
Concept
Coefficient of velocity is the ratio of actual jet velocity at vena contracta to theoretical velocity (2gh)1/2.
Formula
Cv = V / (2gh)1/2
Step-by-step solution
1. Theoretical velocity from Torricelli's theorem: Vth = (2gh)1/2. 2. Actual velocity at vena contracta = V. 3. Cv = actual velocity / theoretical velocity = V / (2gh)1/2. 4. So option B is correct.
Explanation
Because of friction, the real jet velocity is a little less than the ideal velocity (2gh)1/2. The ratio of actual velocity to ideal velocity is called the coefficient of velocity. Its value is usually about 0.95 to 0.99.
Why the other options are wrong
A: wrong power and an extra factor of 4, not a velocity ratio. C: 2Vgh/300 is not dimensionless and has no physical meaning. D: This is inverted and has wrong powers, so it is not a velocity ratio.
Shortcut
Cv must be dimensionless: only V/(2gh)1/2 is a ratio of two velocities.
Common mistake
Using 2gh without the square root, or writing the ratio upside down (theoretical/actual).
Correct answer: B) V / (2gh)^(1/2)