Q.90 The Cd value of an orifice of d/D = 0.5 (d = diameter of orifice and D = diameter of the pipe) lies in the range
- A0.60 to 0.62Correct
- B0.95 to 0.98
- C0.70 to 0.80
- D0.81 to 0.94
Solution
Concept
An orifice meter has a sharp-edged opening, so the jet contracts strongly (vena contracta). This gives a low Cd of about 0.6 to 0.62.
Formula
Q = Cd × a0 × a1 × √(2gh) / √(a12 − a02)
Step-by-step solution
1. An orifice meter is a thin plate with a sharp-edged hole placed in a pipe. 2. The flow contracts after the orifice (vena contracta), so the area of the jet is much smaller than the orifice area. 3. Because of this contraction and the energy losses, Cd is low. 4. For d/D around 0.5, Cd is about 0.60 to 0.62.
Explanation
An orifice meter causes a sudden contraction and large energy loss. The jet area at the vena contracta is much less than the orifice area. So its Cd is low, about 0.60 to 0.62 for d/D = 0.5.
Why the other options are wrong
B: 0.95 to 0.98 is the typical Cd of a venturimeter. C: 0.70 to 0.80 is too high for a sharp-edged orifice and is closer to a flow nozzle. D: 0.81 to 0.94 is in the range of nozzles or mouthpieces, not orifices.
Shortcut
Remember: orifice about 0.62, nozzle about 0.95 to 0.98, venturi about 0.96 to 0.98.
Common mistake
Confusing the Cd of an orifice meter with that of a venturimeter.
Correct answer: A) 0.60 to 0.62