Bernoulli’s Equation

Pressure energy, kinetic energy and potential energy are the three main types of energy associated with fluid flow.

Pressure energy: This is of higher value in aircraft hydraulic systems.

    m = mass (kg)

    p = pressure (Nm2 or Pa)

    ρ = density of the fluid (kg/m³)

Kinetic energy: This is the energy stored in a moving body.

    m = mass (kg)

    v = velocity of the fluid (m/s)

Potential energy: This is the energy, which is possessed by a body by virtue of its position in a force field.

    g = gravitational acceleration (m/s²)

    h = height (m)

        The total energy level of the fluid flow remains constant unless work is done on a fluid when it moves from one point to another. Bernoulli’s equation is a statement of energy conservation principle appropriate for flowing fluids. This qualitative behaviour of lowering of fluid pressure in regions where the flow velocity is increased is known as Bernoulli Effect.

        Based on the above energy equations, the following Bernoulli’s equation is derived.

The Venturi Tube

It is a practical application of Bernoulli’s equation, used for measuring the quality of liquid flow in a pipeline. The tube has a reduction in cross sectional area from the mouth of the tube to the throat. The gradual increase in cross section from the throat to the outlet avoids turbulence. While measuring, the manometer tubes are positioned at the mouth and throat. As the fluid flows through the venture, the reading on the manometer tube is less than the pressure reading. The manometer tubes are replaced by U-tubes in case of gases. The venture tube diagram is shown below.

        The same principle is applies on the theory of lift on an aerofoil at the aircraft wing. The greater velocity across the upper surface produces a decrease in pressure and subsequent lift.