Fluid Flow in Pipe

At the pump we will meet Bernoulli equation. This equation is the conservation energy of fluid so as to approximate a pump installation should consider kinetic energy and potential energy.

(P/ρ) + (V²/2) + gz = constant

For ideal fluid, friction is ignored.

(P₁/ρg) + (V₁²/2g) + z₁ = (P₂/ρg) + (V₂²/2g) + z₂ = constant

Energy equation and head equation can be written as follows:

Energy equation

m{(P₁/ρ) + (V₁²/2) + gz₁} + W_shaft = m{(P₂/ρ) + (V₂²/2) + gz₂} + m.g Σ(head loss total)

Head equation

{(P₁/ρg) + (V₁²/2g) + z₁} + H_shaft = {(P₂/ρg) + (V₂²/2g) + z₂} + ΣHl_total

At the amount of total head loss is divided into two parts between major head loss  and minor head loss. Major head loss is head loss due to surface roughness, pressure drop and length of pipe flow.

h_{major loss} = f . (L/D) . (V²/2)

where:

f           = friction factor

L          = Length of pipe

D         = Diameter of pipe

V         = flow velocity

g          = Acceleration of gravity = 9.81 m/s²

While minor head loss is head loss due to fitting of elbow, gate valve, check valve, change in cross section flow and straight. This head loss due to components that are intentionally installed and have different function.

H_{minor loss} = k . (V²/2)

k = f . (L_e/D)

The value of f is obtained by using Reynolds number contained in the Moody chart, while Le/D is obtained from the table component.