# Differential pressure and velocity relationship

### How to Convert Differential Pressure to Flow | Sciencing

The equation of continuity states that for an incompressible fluid Bernoulli's equation does, relating the pressure, velocity, and height of a fluid. Pressure and velocity have an inverse relation an example pumps are used to to increase the velocity of the fluids in case when water flows from a river to a. One of the cornerstones of this field is Bernoulli's equation, named for To find the velocity of the fluid flow, multiply the differential pressure by.

This is the second equation and relates ambient atmospheric pressure and temperature to density. Assuming average conditions of 70 F and a barometer of If, for example, we measure a differential pressure from the pitot tube of 2.

Air velocity is a function of air density and differential pressure, but determining air flow requires that the geometry of the piping be taken into account. Note that it is still critical that the pitot tube be installed so that it is pointed directly into the oncoming flow stream.

Ideally, determining the flow in terms of volume should simply a matter of multiplying the cross sectional area of the tube or duct by the air velocity. If the dimensions of the ducting are known, then the cross-sectional area can be easily determined and the volumetric flow calculated. There is a problem with this, however — the velocity of the air is not uniform at all points along the cross-sectional area of the tube.

This is because friction between the moving air and the inside surface of the pipe or duct slows the velocity down. 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.

### Basics of Air Velocity, Pressure and Flow

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. It is this pressure difference, in fact, that causes the fluid to flow faster at the place where the pipe narrows.

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

A geyser Consider a geyser that shoots water 25 m into the air. How fast is the water traveling when it emerges from the ground? If the water originates in a chamber 35 m below the ground, what is the pressure there? To figure out how fast the water is moving when it comes out of the ground, we could simply use conservation of energy, and set the potential energy of the water 25 m high equal to the kinetic energy the water has when it comes out of the ground.

Another way to do it is to apply Bernoulli's equation, which amounts to the same thing as conservation of energy. Let's do it that way, just to convince ourselves that the methods are the same.

But the pressure at the two points is the same; it's atmospheric pressure at both places. We can measure the potential energy from ground level, so the potential energy term goes away on the left side, and the kinetic energy term is zero on the right hand side.

This reduces the equation to: If the fluid is flowing up to a higher elevation, this energy conversion will act to decrease the static pressure. If the fluid flows down to a lower elevation, the change in elevation head will act to increase the static pressure.

Conversely, if the fluid is flowing down hill from an elevation of 75 ft to 25 ft, the result would be negative and there will be a Pressure Change due to Velocity Change Fluid velocity will change if the internal flow area changes. For example, if the pipe size is reduced, the velocity will increase and act to decrease the static pressure. If the flow area increases through an expansion or diffuser, the velocity will decrease and result in an increase in the static pressure.

If the pipe diameter is constant, the velocity will be constant and there will be no change in pressure due to a change in velocity. As an example, if an expansion fitting increases a 4 inch schedule 40 pipe to a 6 inch schedule 40 pipe, the inside diameter increases from 4.