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.
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.