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# Pressure Drop Formula

When fluid flows through some pipe, then there will be a pressure drop that occurs due to the result of resistance to flow. There may also be a gain or loss of pressure due to the change in elevation between the start and end of the pipe. This overall pressure difference across the pipe is caused by many factors. Such as friction between the fluid and the wall of the pipe, friction between adjacent layers of the fluid itself, friction loss as the fluid passes through any pipe fittings, bends, valves, or components. This loss or drop in pressure is due to the change in elevation of the fluid (if the pipe is not horizontal). This topic will explain the pressure drop formula with examples. Let us learn it!

## Concept of Pressure Drop

The pressure drop will describe the difference in the pressure between two points of a network carrying fluid. The pressure drop will occur while the frictional force caused by the resistance to flow acting on the fluid as it flows through the tube.

This drop in pressure has a relation between viscosity and velocity of the liquid. The main factors that determine the resistance to the liquid flow are fluid velocity through the pipe and the fluid viscosity. Pressure drop is in some proportional to the frictional shear forces within the pipe network.

Therefore, the Pressure drop is the quantity of line pressure, which is the lost forever when gas flows through a device in a gas line. This loss of pressure is caused by the frictional resistance of the parts exposed to the gas. Each instrument and fitting cause some certain amount of drop in pressure.

## Pressure Drop Calculations

Pressure drop is possible because of elevation changes and turbulence caused by abrupt changes in direction, as well as due to friction within the pipe and fittings. The most common methods that will be used to determine the head loss in the fiberglass pipe are based on Darcy-Welsbach equations. The suitability of each method depends on the type of flow due to the gravity or pumped and the level of accuracy required.

### The Pressure Drop Formula:

The Pressure drop is denoted by the symbol J.

The pressure drop formula is given by, J = $$\frac{f\;L\;v^2} {2g\;D}$$

• J = pressure drop
• f = friction factor
• L = length of the tube
• v = velocity of the fluid
• g = acceleration due to gravity
• D = inner diameter of the tube

## Solved Examples for Pressure Drop Formula

Q.1: Compute the pressure drop of a fluid whose velocity is 60 m per sec. The length of the tube is 20 m, the inner diameter is 0.1m, and the friction factor is 0.5. Use Pressure Drop Formula.

Solution: Given parameters are,

• f = 0.5
• L = 20 m,
• v = 60 m per sec,
• g = 9.8 m per sec,
• D = 0.1 m

Pressure drop formula will be, J = $$\frac{f\;L\;v^2} {2g\;D}$$

= $$\frac{0.5 \times 20 \times 60^2} {2\times 9.8 \times 0.1}$$

= $$\frac{36000}{1.96}$$

= 18367.34 Pa

Q.2: Compute the pressure drop of a liquid having flow of 10 m per sec. The length of the tube is 4m, the inner diameter is 0.5 m and the friction factor is 0.3.

Solution: Given parameters are,

• f = 0.3,
• L = 4 m,
• v = 10 m per sec,
• g = 9.8 m per sec,
• D = 0.5 m

Pressure drop formula will be,

$$J = \frac{f\;L\;v^2} {2g\;D}$$

$$J = \frac{0.3 \times 4 \times 10^2} {2\times 9.8 \times 0.5}$$

$$J = 12.24 Pa.$$

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