Question

Take water density and kinematic viscosity as p=1000 kg/m3 and v= 1x10^-6 m^2/s. (c) Water flows through an orifice plate with a loss coefficient, Ko, of 10 and diameter of Do= 45 mm. The flow is controlled by a gate valve downstream of the plate with a pipe diameter Dy 1.5Do. Assuming that the total head drop across both components is Δhtotal=25 m, determine the loss coefficient of the valve to maintain a flow rate through the system of 10 I/s. Ignore the friction loss.

Answer 1

Answer:

$K_v=12.34$

Explanation:

Given;

For orifice, loss coefficient, K₀ = 10

Diameter, D₀ = 45 mm = 0.045 m

loss coefficient of the orifice, Ko = 10

Diameter of the gate valve, Dy = 1.5D₀ = 1.5 × 0.045 m = 0.0675 m

Total head drop, Δhtotal=25 m

Discharge, Q = 10 l/s = 0.01 m³/s

Now,

the velocity of flow through orifice, Vo =   Discharge / area of the orifice

or

Vo = $\frac{0.01}{\frac{\pi}{4}0.045^2}$

or

Vo = 6.28 m/s

also,

the velocity of flow through gate valve, $V_v$ =   Discharge / area of the orifice

or

$V_v$ = $\frac{0.01}{\frac{\pi}{4}0.0675^2}$

or

$V_v$ = 2.79 m/s

Now,

the total head drop = head drop at orifice + head drop at gate valve

or

25 m = $K_o\frac{V_o^2}{2g}+K_v\frac{V_v^2}{2g}$

where,

$K_v$ is the loss coefficient for the gate valve

on substituting the values, we get

25 m = $10\frac{6.28^2}{2\times 9.81}+K_v\frac{2.79^2}{2\times9.81}$

or

$K_v\frac{2.79^2}{2\times9.81}$ = 4.898

or

$K_v=12.34$