Discussion
Starting from the first principles, the expression for discharge of a liquid (Q) through a venturimeter is given by:
Where, Q = discharge in m3/s
K = discharge coefficients
C = constant of venturimeter
h = venturi head in meters of a fluid flowing through venturimeter
Answer: C
The discharge is \(Q = KCh^{1/2}\).
Applying Bernoulli's equation and continuity between the inlet and the throat gives the theoretical discharge:
\[ Q_{th} = \frac{a_1 a_2}{\sqrt{a_1^2 - a_2^2}} \sqrt{2gh} \]
Everything except \(\sqrt{h}\) is fixed for a given meter, so it is grouped as the meter constant C, and the discharge coefficient K allows for losses: \(Q = KC\sqrt{h}\). Discharge must grow as the square root of the head, so the forms with h to the first power, or with roots on K or C, are wrong.
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