Fluid Mechanics
Bernoulli's Equation — Flow in Pipes
Apply Bernoulli's principle to calculate pressure, velocity and elevation changes in pipe systems. Foundation of all fluid mechanics calculations.
Units:
Bernoulli's equation assumes ideal (inviscid) flow. Real systems have friction losses — add the head loss term h_L. At high velocities (Re > 4000) turbulent losses dominate and must be calculated separately with Darcy-Weisbach.
P₁/ρg + v₁²/2g + z₁ = P₂/ρg + v₂²/2g + z₂ + h_L [Bernoulli + head loss]
Input
Pressure at point 1 iGauge pressure at the upstream measurement point in bar.
bar
Velocity at point 1 iFluid velocity at the upstream point in m/s.
m/s
Elevation at point 1 iHeight of point 1 above reference datum in metres.
m
Velocity at point 2 iFluid velocity at the downstream point in m/s.
m/s
Elevation at point 2 iHeight of point 2 above reference datum in metres.
m
Head loss h_L iTotal friction and minor head losses between the two points in metres of fluid head.
m
Fluid density ρ iFluid density. Water: 1000, Hydraulic oil: 870, Diesel: 840 kg/m³.
kg/m³
Result
Pressure at point 2 [bar]
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Pressure at point 2 [kPa]
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Pressure head at 1 [m]
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Pressure head at 2 [m]
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Total head at 1 [m]
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Total head at 2 [m]
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