Question

A 5 cm diameter orfice discharges fluid from a tank with a head of 5 meters. The discharge rate, Q, is measured at 0.015 m^3/s. The actual velocity at the vena contracta is 9 m/s. The coefficient of discharge is nearest to:________

Answer 1

Answer:

$\mathbf{ C_d = 0.86}$

Explanation:

Given that:

diameter of the orifice D = 5 cm = 5 × 10⁻² m

discharge rate Q = 0015 m³/s

Actual velocity V = 9 m/s

By using the formula

$Q = C_d \times A \times \sqrt{2gh}$

where;

$v = \sqrt{2gh}$ = 9  m/s

$Q = C_d \times A \times v}$

where;

$A = \dfrac{\pi D^2}{4}$

$A = \dfrac{\pi (5 \times 10^{-2} ) ^2}{4}$

$A = 0.00196 \ m^2$

Again,

$Q = C_d \times A \times v}$

$0.015 = C_d \times 0.00196 \times 9$

$C_d = \dfrac{0.015 }{ 0.00196 \times 9}$

$\mathbf{ C_d = 0.86}$

Hence, the coefficient of discharge $\mathbf{ C_d = 0.86}$