Engr Help

Comparison between Pumps and Turbines

Centrifugal Pumps Radial Flow Reaction Turbines

Pump adds energy to the fluid.	Turbine extracts energy from the fluid.
Pump increases the head.	Turbine decreases the head.
Power added to fluid.	Power extracted from fluid.
Pressure increased by pump.	Pressure decreased by turbine.
T_z = external torque driving pump	T_z = torque developed by turbine
Q = 2π r₁ b₁ V_r1 = 2π r₂ b₂ V_r2	Q = 2π r₁ b₁ V_r1 = 2π r₂ b₂ V_r2
T_z = ρ Q [( r₂ V_t2 ˗ r₁ V_t1 ]	T_z = ρ Q [( r₂ V_t2 ˗ r₁ V_t1 ]
P = Power = T_z ω	P = Power = T_z ω
H = Head = P / Q γ	H = Head = P / Q γ
∆P = γ H + (1/2)ρ V₁²˗ (1/2) ρ V₂²	∆P = γ H + (1/2)ρ V₂² ˗ (1/2) ρ V₁ ²
Station 1 refers to inner radius. (inlet)	Station 1 refers to outer radius. (inlet)
Station 2 refers to outer radius. (exit)	Station 2 refers to inner radius. (exit)

Definition of Terms:

V_r1	Radial component of the absolute fluid velocity at station 1
V_r2	Radial component of the absolute fluid velocity at station 2
V_t1	Tangential component of the absolute fluid velocity at station 1
V_t2	Tangential component of the absolute fluid velocity at station 2
r₁	Radial distance to station 1
r₂	Radial distance to station 2
b₁	Height at station 1
b₂	Height at station 2
T_z	External torque driving a pump
T_z	Torque developed by turbine by changing angular momentum of fluid
Q	Flow rate passing through a pump or turbine
ω	Angular speed of pump or turbine; rotational rate
P	Power added to fluid by pump
P	Power extracted from fluid by turbine
H	Head added to fluid by the pump
H	Head extracted from the fluid by the turbine
ρ	Mass density of the fluid
γ	Specific weight of the fluid
∆P	Pressure rise caused by pump ∆P = P₂ ˗ P₁
∆P	Pressure drop caused by turbine ∆P = P₁ ˗ P₂
β ₁	Angle between the vane at station 1 and the tangent to the circle at station 1
β₂	Angle between the vane at station 2 and the tangent to the circle at station 2
α₁	Angle between the guide vane at station 1 and the vane of the impeller at station 1, turbine