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

`\mathbf{ C_d = 0.86}`

Step-by-step 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 * A * √(2gh)`

where;

`v = √(2gh)` = 9 m/s

`Q = C_d * A * v}`

where;

`A = (\pi D^2)/(4)`

`A = (\pi (5 * 10^(-2) ) ^2)/(4)`

`A = 0.00196 \ m^2`

Again,

`Q = C_d * A * v}`

`0.015 = C_d * 0.00196 * 9`

`C_d = (0.015 )/( 0.00196 * 9)`

`\mathbf{ C_d = 0.86}`

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