# Relationship between head loss flow rate

### Losses in Pipes The peak flow can be obtained from the parabolic flow relationship. For " pressure head" I assume you mean frictional pressure loss. The answer depends on. In fluid dynamics, the Darcy–Weisbach equation is an empirical equation, which relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow . The relationship between mean flow velocity ⟨v⟩ and volumetric flow rate Q is. Q = A ⋅ ⟨ v ⟩, {\displaystyle Q=A\cdot . Thus, it is often useful to estimate the relationship as the head being directly For laminar flow, the head loss is proportional to velocity rather than velocity.

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. 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.

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. In a pump, liquid horsepower is inputted and converted to velocity energy by the impeller, then converted to pressure energy in the diffuser section of the volute case to push liquid through the piping to the sprinkler or holding tank or cooling coils or whatever is attached to it. To do this work we have to supply the pump a given amount of energy. If you want to move something, there will be resistance. 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. 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.

• Darcy–Weisbach equation
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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. It attaches itself to any surface and cannot be moved.

### Relationship Between Pipe Size and Friction: 5. Basic Irrigation Concepts

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.

## Losses in Pipes

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. 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. The effect is similar to attaching a smaller diameter pipe in the system. The velocity of the liquid increases and the head loss due to friction increases. Energy Loss Any time a liquid is asked to change direction or to change velocity there is a change in energy.

The energy lost by the liquid is converted to heat created by friction. Since the amount of liquid exiting a pipe has to equal the amount entering the pipe, the velocity must be equal. If the velocity is equal, then the velocity energy head must be equal. This only leaves one place for the energy to come from: The measured pressure entering the pipe will be higher than the measured pressure exiting the pipe.

Friction Loss Tables In an effort to easily predict the head loss in pipes and fittings, there were a number of studies made many years ago. These have been published, as formulas and tables, for different size pipes, fittings, and flow ratings. The most common used are "Darcy, Weisbach" and "Williams and Hazen. The "Darcy, Weisbach" tables are based on the head loss in clean, new pipe.