Bernoulli Equation

\frac{p}{γ} + \frac{V ^{2}}{2 g} + z = const + h_{p} - h_{t} - h_{L}

Along a streamline for steady incompressible flow, the sum of pressure, velocity, and elevation heads is constant except for pumps, turbines, and losses. Each term has units of length.

$p / γ$ (m): Pressure head
$V^{2} /2 g$ (m): Velocity head
$h_{L}$ (m): Head loss

Step-by-step solved example

A nozzle discharges to atmosphere from a tank with 5.0 m water surface above the jet. Neglect losses. Jet speed?

p/γ + V²/2g + z = constant along a streamline (inviscid, steady).

1. Torricelli
p = 0 gage both free surface (V≈0) and jet. V = √(2gh) = √98.1 = 9.90 m/s.
$V = 2 g h = 9.90 m/s$

Answer: 9.90 m/s

10 practice questions

0/10 correct

1.Velocity head at 6 m/s is

2.Pitot tube stagnation pressure measures

3.A pump head h_p in Bernoulli

4.If elevation drops 4 m and velocity is unchanged, pressure head

5.Torricelli’s law is a special case of

6.Head loss h_L is always

7.HGL is the plot of

8.Cavitation risk rises when

9.Venturi: throat pressure is

10.Energy grade line falls in the flow direction when