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.

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 =

or

Vo = 6.28 m/s

also,

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

or

=

or

= 2.79 m/s

Now,

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

or

25 m =

where,

is the loss coefficient for the gate valve

on substituting the values, we get

25 m =

or

= 4.898

or

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