Bernoulli’s Equation Formula

The Bernoulli Equation is a different way of the conservation of energy principle, applied to flowing fluids. It relates the pressure, the kinetic energy and the gravitational potential energy of a fluid in a container or flowing in a tube.

Describes the lowering of fluid pressure in regions where the flow velocity is increased. In the high-velocity flow through the constriction, kinetic energy must increase at the expense of pressure energy.

Pressure + ½ density * square of the velocity + density * gravity
acceleration* height = constant

The equation is written

P + ½ ρ v2 +ρ g h = constant

That says the whole formula holds along the system, each term can change but the sum is the same.

We have:

P: Pressure

v: velocity of the fluid

ρ: Density of the fluid

h: height of the container or the pipe here the fluid is flowing

Bernoulli’s Equation Formula Questions:

1) We have a fluid with density 1 Kg/m3 that is moving through a pipe with transverse area 0.1 m2 and a velocity of 3.5 m/s. It is connected to another pipe of 1 m2 of area, both at the same height. The pressure at the beginning of the tube is 2 kPa. What is the pressure of fluid at the end of the second tube?

a. Pf = ?.06 KPa.

2) Consider the same problem above. What is the pressure of fluid at the end of the second tube if the second tube is placed at 1 m over the ground?

a. Pf = -1.74 KPa.

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