# Relationship between flow and pressure in a pipe

### Relationship between Flow Rate and Pressure | Physics Forums

What is the relationship between pressure drop and flow rate (equation wanted)? in which P is related to Volumetric Flowrate of the Pipe from which one can. Calculate volumetric flow rate of ideal gas at different conditions of pressure and Flow in pipes is considered to be laminar if Reynolds number is less than , . where is: M - Mach number M=v/c - relation between local fluid and local. A water hammer is a surging of pressure that occurs when the flow of water in a The Energy Equation expresses the relationship between the energy at two.

## Relationship between Flow Rate and Pressure

If the flow rate through the expansion is gpm, the velocity goes from 9. The change in static pressure across the expansion due to the change in velocity is: In other words, pressure has increased by almost 0. Pressure Change due to Head Loss Since head loss is a reduction in the total energy of the fluid, it represents a reduction in the capability of the fluid to do work. Head loss does not reduce the fluid velocity consider a constant diameter pipe with a constant mass flow rateand it will not be effect the elevation head of the fluid consider a horizontal pipe with no elevation change from inlet to outlet.

### fluid dynamics - Relation between pressure, velocity and area - Physics Stack Exchange

Therefore, head loss will always act to reduce the pressure head, or static pressure, of the fluid. There are several ways to calculate the amount of energy lost due to fluid flow through a pipe. The two most common methods are the Darcy-Weisbach equation and the Hazen-Williams equation. Sciencing Video Vault Confined Energy If pressure equals force divided by area, pressure also equals force times distance divided by area times distance: Area times distance is equivalent to volume, and force times distance is the formula for work, which in this situation, is equivalent to energy.

Thus, the pressure of a fluid can also be defined as energy density: For the simplified case of a fluid that does not change elevation as it flows, total energy is the sum of the energy of the pressure and the kinetic energy of the moving fluid molecules. Conserved Energy The fundamental relationship between pressure and fluid velocity is captured in the Bernoulli equation, which states that the total energy of a moving fluid is conserved.

In other words, the sum of energy due to pressure and kinetic energy remains constant even when the flow volume changes. By applying the Bernoulli equation, you can demonstrate that pressure actually decreases when fluid is traveling through a constriction.

Making fluids flow There are basically two ways to make fluid flow through a pipe.

One way is to tilt the pipe so the flow is downhill, in which case gravitational kinetic energy is transformed to kinetic energy. The second way is to make the pressure at one end of the pipe larger than the pressure at the other end. A pressure difference is like a net force, producing acceleration of the fluid.

### Fluid dynamics and Bernoulli's equation

As long as the fluid flow is steady, and the fluid is non-viscous and incompressible, the flow can be looked at from an energy perspective. This is what Bernoulli's equation does, relating the pressure, velocity, and height of a fluid at one point to the same parameters at a second point.

The equation is very useful, and can be used to explain such things as how airplanes fly, and how baseballs curve.

Bernoulli's equation The pressure, speed, and height y at two points in a steady-flowing, non-viscous, incompressible fluid are related by the equation: Some of these terms probably look familiar If the equation was multiplied through by the volume, the density could be replaced by mass, and the pressure could be replaced by force x distance, which is work.

Looked at in that way, the equation makes sense: For our first look at the equation, consider a fluid flowing through a horizontal pipe.

The pipe is narrower at one spot than along the rest of the pipe. By applying the continuity equation, the velocity of the fluid is greater in the narrow section. Is the pressure higher or lower in the narrow section, where the velocity increases?

Your first inclination might be to say that where the velocity is greatest, the pressure is greatest, because if you stuck your hand in the flow where it's going fastest you'd feel a big force. The force does not come from the pressure there, however; it comes from your hand taking momentum away from the fluid. The pipe is horizontal, so both points are at the same height. Bernoulli's equation can be simplified in this case to: The kinetic energy term on the right is larger than the kinetic energy term on the left, so for the equation to balance the pressure on the right must be smaller than the pressure on the left.