Question

Water is discharged from the vertical side of a tank through a circular orifice of diameter 2 cm under laminar flow conditions. The water surface in the tank is maintained at a constant level above the center of the orifice. If the fluid jet has a diameter of 1.6 cm at its vena contracta, then the coefficient of contraction is ______ (rounded off to two decimal places).

Hint:

Coefficient of contraction is simply the square of the ratio of the jet diameter at the vena contracta to the orifice diameter.

Answer 1

Correct Answer: 0.64

Alternate method: compute the actual areas first, then take the ratio.
Orifice diameter $d_o = 2$ cm, so orifice area:
\[ A_o = \frac{\pi}{4}(2)^2 = \pi \approx 3.1416 \text{ cm}^2 \]

Jet diameter at the vena contracta $d_j = 1.6$ cm, so jet area:
\[ A_j = \frac{\pi}{4}(1.6)^2 = \frac{\pi}{4}(2.56) = 0.64\pi \approx 2.0106 \text{ cm}^2 \]

The coefficient of contraction is the ratio of these two areas:
\[ C_c = \frac{A_j}{A_o} = \frac{2.0106}{3.1416} = 0.64 \]
Working with the actual numerical areas gives the same result, $C_c = 0.64$.