Mechanical Energy Equation vs. Bernoulli Equation

Analyze and compare the Mechanical Energy Equation and Bernoulli Equation for pump/fan and turbine systems, including energy calculations in various forms (per unit mass, volume, and weight).

Calculator

Inputs

Inlet Pressure (Pa)

Outlet Pressure (Pa)

Inlet Velocity (m/s)

Outlet Velocity (m/s)

Density (kg/m³)

Gravity (m/s²)

Inlet Height (m)

Outlet Height (m)

Hydraulic Loss (J/kg)

Results

Inlet Pressure Energy-- J/kg

Outlet Pressure Energy-- J/kg

Inlet Velocity Energy-- J/kg

Outlet Velocity Energy-- J/kg

Inlet Elevation Energy-- J/kg

Outlet Elevation Energy-- J/kg

Required Shaft Energy-- J/kg

Calculator

Inputs

Inlet Pressure (Pa)

Outlet Pressure (Pa)

Inlet Velocity (m/s)

Outlet Velocity (m/s)

Specific Weight (N/m³)

Inlet Height (m)

Outlet Height (m)

Loss Head (m)

Results

Inlet Pressure Head-- m

Outlet Pressure Head-- m

Inlet Velocity Head-- m

Outlet Velocity Head-- m

Required Shaft Head-- m

Calculator

Inputs

Inlet Pressure (Pa)

Outlet Pressure (Pa)

Inlet Velocity (m/s)

Outlet Velocity (m/s)

Density (kg/m³)

Gravity (m/s²)

Inlet Height (m)

Outlet Height (m)

Hydraulic Loss (J/kg)

Results

Shaft Energy Output-- J/kg

Calculator

Inputs

Shaft Energy (Pump/Fan) (J/kg)

Hydraulic Loss (J/kg)

Shaft Energy (Turbine) (J/kg)

Hydraulic Loss (Turbine) (J/kg)

Results

Pump/Fan Efficiency--

Turbine Efficiency--

Equation Form	Pump/Fan	Turbine	Dimensions	Notes
Energy per Unit Mass	pin/ρ + vin²/2 + ghin + Eshaft = pout/ρ + vout²/2 + ghout + Eloss	pin/ρ + vin²/2 + ghin = pout/ρ + vout²/2 + ghout + Eshaft + Eloss	J/kg (m²/s²)	Extended Bernoulli Equation with losses and work
Energy per Unit Volume	pin + ρvin²/2 + γhin + ρEshaft = pout + ρvout²/2 + γhout + ρEloss	N/A	Pa (N/m²)	Multiply energy per unit mass by density ρ
Energy per Unit Weight (Head)	pin/γ + vin²/2g + hin + hshaft = pout/γ + vout²/2g + hout + hloss	N/A	m (head)	Divide energy per unit mass by gravity g