What is the effect of vena contracta on discharge measurement across an orifice?

• A. The actual discharge is higher than the theoretical discharge.
• B. The actual discharge equals the theoretical discharge.
• C. The effective flow area equals the orifice area.
• D. Due to vena contracta, the discharge coefficient drops below unity, making the actual discharge lower than the ideal.

Answer: (D)

The key idea is that flow through an orifice is not ideal because the jet contracts to a narrower area just downstream, called the vena contracta. This smaller cross-section means the real flow is not the same as the simple, frictionless calculation would predict. To account for this, engineers use a discharge coefficient, C_d, which multiplies the ideal discharge. For a real orifice, C_d is less than 1 because of the energy losses and the reduced effective flow area at the vena contracta. Therefore the actual discharge is lower than the ideal discharge. The higher velocity at the vena contracta doesn't translate into more flow overall because the losses reduce the usable flow rate that can be collected downstream.