Bernoullis Equation Formula

What Is Bernoulli’s equation?

Water in a hydraulic system exhibits two types of energy – kinetic and potential. Kinetic energy when water is in motion and potential is when there is water pressure. The sum of both kinetic and potential forms is the total energy of water. According to Bernoulli’s principle, the total energy of the liquid remains constant and hence when water flows in a system increases, the pressure must decrease.

Bernoulli’s principle states that for an inviscid flow of a non-conducting fluid, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or decrease in the potential energy. Bernoulli’s principle can be applied to various types of liquid flow, resulting in what is denoted as Bernoulli’s equation. The simple form of Bernoulli’s principle is applicable for incompressible flows.

Bernoulli’s Equation Formula

Following is the formula of Bernoulli’s equation:

 $P+\frac{1}{2}\rho v^{2}+\rho gh=constant$

Where,

• P is the pressure
• v is the velocity of the fluid
• ρ is the density of the fluid
• h is the height of the pipe from which the fluid is flowing

Solved Example

Example 1

A pipe has an internal diameter of 2.2 cm and a pressure of 2.5 x 105 Pa supplies water into a house. Calculate the pressure of flow in the pipe which enters with an inlet pipe diameter of 1.5 cm at a height of 5m above ground. The inlet pipe flow speed is 1.8 m / s.

Solution

v2 =a1v1 / a2 or (pie) ∗ (1.1)2

= 2.178 / 0. 5625

=3.872 m/s

P2 = 2.5∗105 Pa – 1/2[1∗103 kg/m3] [14.99 − 3.24] – [1 * 103] [9.8] [5]

P2= (2.5 x 105) – (5.88 x 103) – (49 x 103)Pa

P2 = 1.95 * 105 Pa

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