# Head loss and flow rate relationship

### Friction loss - Wikipedia

Relationship Between Pressure Drop and Flow Rate in a Pipeline Head loss is a reduction in the capability of the fluid to do work and will act. SPT at a range of flow rates through the SPT provide data from which a mathematical relationship between flow rate and head loss can be established for the. In fluid flow, friction loss (or skin friction) is the loss of pressure or “head” that occurs in pipe or The Yamal–Europe pipeline carries methane at a volume flow rate of × m3 of gas per year, at Reynolds numbers greater than 50 × 10 6. .. A graphical depiction of the relationship between Δp / L, the pressure loss per.

If you try to push a heavy box along the ground, it will require a certain amount of effort to do it. Since the weight and the size of the box will not change, the work required should be the same regardless of the surface it is resting on. However, the box will be much easier to move on a smooth linoleum floor than trying to move it on a deep pile carpet. The difference in the required effort is due to friction.

- Friction loss
- Darcy–Weisbach equation

The carpet has a higher resistance to the movement of the box than the smooth floor. To move a given volume of liquid through a pipe requires a certain amount of energy.

An energy or pressure difference must exist to cause the liquid to move. A portion of that energy is lost to the resistance to flow. This resistance to flow is called head loss due to friction. Forms of Flow Resistance Head Loss due to Friction One form of resistance to flow is due to the viscosity of the liquid. Viscosity is the amount of work needed to move one "box" of liquid against another "box" of liquid.

Every liquid has its own value for this resistance to flow. The values for water are lower than for the motor oil. Another characteristic of any liquid is its attraction to a surface.

### Losses in Pipes

It attaches itself to any surface and cannot be moved. The liquid in the "box" on the very surface of a pipe does not flow or move. It always remains stationary. The liquid in the "box" above it has to slide against it and that requires an amount of energy to overcome friction between the two "boxes. A layer is formed by this non-moving liquid and reduces the inside diameter of the pipe. This increases the velocity of the liquid passing through it.

The liquid is not moving at the pipe wall but has a much higher velocity at the center of the pipe. The condition of the inside of a pipe also has a great effect on the head loss of the flow of liquid. The rougher it is, the thicker the layer of non-moving or slow moving liquid near the pipe wall.

This reduces the inside diameter of the pipe, increasing the velocity of the liquid. With the increase in velocity comes an increase in friction losses. Pipe Fittings Any time a liquid flow changes direction there is resistance. Since all liquids have weight, they also have momentum.

## Losses in Pipes

This means the liquid will always try to continue moving in the same direction. When the liquid encounters a change in direction such as an elbowits momentum carries the flow to the outer edge of the fitting.

Because the liquid is trying to flow around the outer edge of the fitting, the effective area of the fitting is reduced. 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. Like pipe friction, these losses are roughly proportional to the square of the flow rate.

### Darcy–Weisbach equation - Wikipedia

Defining K, the loss coefficient, by allows for easy integration of minor losses into the Darcy-Weisbach equation. K is the sum of all of the loss coefficients in the length of pipe, each contributing to the overall head loss.

Although K appears to be a constant coefficient, it varies with different flow conditions. Factors affecting the value of K include: Tabulated values of K are for components in isolation - with long straight runs of pipe upstream and downstream. Some very basic information on K values for different fittings is included with these notes and in most introductory fluid mechanics texts.

For more detail see e.