A 15 cm diameter orifice discharging from a tank issues out a jet of diameter 12.75 cm diameter at a vena contracta. The coefficient of contraction is:
- A0.62
- B0.85
- C0.682
- D0.722Correct
Solution
Concept
Coefficient of contraction = area of jet at vena contracta / area of orifice.
Formula
Cc = ac / a = (dc / d)2
Step-by-step solution
1. Orifice diameter d = 15 cm. Jet diameter at vena contracta dc = 12.75 cm. 2. Cc = (dc / d)2 = (12.75 / 15)2 3. 12.75 / 15 = 0.85 4. Cc = 0.852 = 0.7225 ≈ 0.722
Explanation
The jet contracts after leaving the orifice. The smallest section is the vena contracta. Cc is the ratio of areas, so we must square the diameter ratio.
Why the other options are wrong
A: 0.62 is the typical Cd of a sharp orifice, not this Cc. B: 0.85 is only the diameter ratio. It is not squared. C: 0.682 does not match the given data.
Shortcut
Cc = (12.75/15)2 = 0.852 = 0.7225.
Common mistake
Taking the diameter ratio 0.85 as Cc without squaring it.
Correct answer: D) 0.722