# Hydraulic pressure and flow relationship

### Hydraulic analogy - Wikipedia The electronic–hydraulic analogy is the most widely used analogy for "electron fluid" in a metal Flow and pressure variables can be calculated in both steady and transient fluid flow A slightly different paradigm is used in acoustics, where acoustic impedance is defined as a relationship between pressure and air speed. To understand the relationship between the pressure drop across a pipeline and the flow rate through that pipeline, we need to go back to one. Of all the concepts that keep parts changers from becoming hydraulic troubleshooters, understanding the difference between pressure and flow is the most.

Total Fluid Energy Daniel Bernoulli, a Swiss mathematician and physicist, theorized that the total energy of a fluid remains constant along a streamline assuming no work is done on or by the fluid and no heat is transferred into or out of the fluid. The total energy of the fluid is the sum of the energy the fluid possesses due to its elevation elevation headvelocity velocity headand static pressure pressure head.

The energy loss, or head loss, is seen as some heat lost from the fluid, vibration of the piping, or noise generated by the fluid flow.

Between two points, the Bernoulli Equation can be expressed as: In other words, the upstream location can be at a lower or higher elevation than the downstream location. 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.

### Fluid Power Formulas, Hydraulics - Engineer's Handbook

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.

Two paradigms can be used to introduce the concept to students using pressure induced by gravity or by pumps. In the version with pressure induced by gravity, large tanks of water are held up high, or are filled to differing water levels, and the potential energy of the water head is the pressure source. This has the advantage of associating electric potential with gravitational potential. A second paradigm is a completely enclosed version with pumps providing pressure only and no gravity.

This is reminiscent of a circuit diagram with a voltage source shown and the wires actually completing a circuit. This paradigm is further discussed below. Other paradigms highlight the similarities between equations governing the flow of fluid and the flow of charge.

• Basic Hydraulic Formulas

Flow and pressure variables can be calculated in both steady and transient fluid flow situations with the use of the hydraulic ohm analogy. The pressure and volume flow variables are treated as phasors in this definition, so possess a phase as well as magnitude.

In this paradigm, a large cavity with a hole is analogous to a capacitor that stores compressional energy when the time-dependent pressure deviates from atmospheric pressure. A hole or long tube is analogous to an inductor that stores kinetic energy associated with the flow of air. Hydraulic analogy with horizontal water flow[ edit ] Voltage, current, and charge[ edit ] Hydraulic pressure difference In general, electric potential is equivalent to hydraulic head.

This model assumes that the water is flowing horizontally, so that the force of gravity can be ignored. In this case electric potential is equivalent to pressure.

Fluids in Motion: Crash Course Physics #15

The voltage or voltage drop or potential difference is a difference in pressure between two points. Electric potential and voltage are usually measured in volts.

Electric current is equivalent to a hydraulic volume flow rate ; that is, the volumetric quantity of flowing water over time.

Usually measured in amperes.

## Hydraulic analogy

Electric charge is equivalent to a quantity of water. Basic circuit elements[ edit ] Conducting wire: Node in Kirchhoff's junction rule: A pipe tee filled with flowing water. A relatively wide pipe completely filled with water is equivalent to conducting wire. When comparing to a piece of wire, the pipe should be thought of as having semi-permanent caps on the ends.

### The Difference Between Pressure and Flow | GPM HYDRAULIC CONSULTING, INC.

Connecting one end of a wire to a circuit is equivalent to un-capping one end of the pipe and attaching it to another pipe. With few exceptions such as a high-voltage power sourcea wire with only one end attached to a circuit will do nothing; the pipe remains capped on the free end, and thus adds nothing to the circuit.

A resistor is equivalent to a constriction in the bore of the pipe which requires more pressure to pass the same amount of water. All pipes have some resistance to flow, just as all wires have some resistance to current. A node or junction in Kirchhoff's junction rule is equivalent to a pipe tee. The net flow of water into a piping tee filled with water must equal the net flow out.

## The Difference Between Pressure and Flow

Voltage or current source: A dynamic pump with feedback control. A capacitor is equivalent to a tank with one connection at each end and a rubber sheet dividing the tank in two lengthwise  a hydraulic accumulator. When water is forced into one pipe, equal water is simultaneously forced out of the other pipe, yet no water can penetrate the rubber diaphragm.

Energy is stored by the stretching of the rubber. As more current flows "through" the capacitor, the back-pressure voltage becomes greater, thus current "leads" voltage in a capacitor. As the back-pressure from the stretched rubber approaches the applied pressure, the current becomes less and less.