Bernoulli’s Principle and Horizontal Pipe Narrows

Question

What is Bernoulli’s Principle and what does it tell us about when a horizontal pipe narrows?

Answer

This principle is based on the conservation of energy in a fluid flow, stating that the sum of all forms of energy must have a constant value along a streamline. In this case it is assumed that the fluid is incompressible (i.e., that the density is constant). The kinetic energy is represented by ½ρν2, the gravitational potential energy is ρgz, and the internal energy is represented by the pressure, p. By dividing each of these by ρg, the principle can be expressed as the total head or the energy head of the system:

$$ H= z + frac{p}{ρg} + frac{v^2}{2g} $$

This can be used to explain some fundamental principles of fluid flow, such as what happens when a pipe narrows. The volumetric flow-rate Q is the product of cross sectional area, A, and flow velocity, v. As such, when A decreases, with constant flow-rate, v must increase, and as the height, z, is constant, the internal energy (i.e., the pressure of the fluid) must decrease.

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