Problem: A 12-in.-diameter pipe is connected to a 6-in.-diameter pipe. The velocity of the water in the 12-in. pipe is 3 fps. What is the velocity in the 6-in. pipe?

Solution: Using the equation A1V1 = A2V2, first determine the area of each pipe:

12-in. diameter:

6-in. diameter:

A = 3.14 x (0.5 ft)2/4 = 0.196 ft2 The continuity equation now becomes:

Solving for V2,

2 0.196 ft2


When water runs through a pipe and the pressure (called pressure head) is measured at various points along the flow, pressure decreases with distance from the source. This pressure decrease is the result of friction loss. Water flow is retarded by the friction of the water against the inside of the pipe. The resistance to flow offered by pipe friction depends on the size (diameter) of the pipe, the roughness of the pipe wall, and the number and type of fittings (e.g., bends, valves) along the pipe run.

Note: Each type of fitting exerts a specific head loss upon the velocity of water through the fitting. For instance, the head loss through a check valve is 2.25 times greater than through a 90° elbow and 10 times greater than the head loss through an open gate valve.

The resistance to flow offered by friction also depends on the speed of the water through the pipe; the more water you try to pump through a pipe, the more pressure it will take to overcome the friction. The resistance can be expressed in terms of the additional pressure required to push the water through the pipe, in either psi or feet of head. Because it is a reduction in pressure, it is often referred to as friction loss or head loss. Head loss is the loss of energy due to friction; the energy is lost as heat. Friction loss is usually measured in feet per 1000 feet of pipe and may easily be converted to pressure loss in pounds per square inch (psi). Factors that affect friction loss include:

• Increased flow rate

• Increased pipe length

• Decreased pipe diameter

• Constricted pipe

• Addition of bends, fittings, and valves

• Smoothness or roughness of the interior surface of pipe

Note: (1) If the flow through a pipe is doubled, the friction loss in the pipe will be decreased by almost four times (obviously, this factor more than any other single factor affects head loss). (2) The diameter of a pipe determines the area of wall in contact with flowing water; for a given discharge, the diameter also determines the velocity of the water.

Pumps are designed to operate under specific head conditions. In addition to the static head, all friction losses and minor losses should be computed in order to determine the total head against which the pump will operate. The total pressure provided at the discharge side of the pump represents the discharge pressure of the discharge head. Head loss from fittings is calculated by substituting the equivalent length of pipe from tables.

Basic terms used in pumping hydraulics include the following:

• Static head is the distance between the suction and discharge water levels when the pump is not in operation. Static head conditions are often indicated by the letter Z:

Static Head = Discharge Elevation - Supply Elevation (9.5)

• Suction lift is the distance between the suction water level and the center of the pump impeller. This term is used only when the pump is in a suction lift condition. In practice, a pump is said to be in a suction lift condition any time the eye (center) of the impeller is above the water being pumped.

• Suction head is the distance between the suction water level and the center of the pump impeller when the pump is in a suction head condition (i.e., any time the impeller is below the water level being pumped).

• Velocity head is the amount of energy required by the pump and motor to overcome the tendency of water to remain at rest or in motion (inertia):

Velocity Head (ft) = Energy losses to maintain velocity (9.6)

• Total dynamic head (TDH) is the static head (the elevation difference) plus the friction head (pressure losses due to the water moving through the pipes) in a given pipe system. Simply, it is the difference in water pressure between the beginning of the pipe (at the pump) and the end of the pipe (i.e., the end point, such as the tank being filled or the consumer's tap). It is the pressure the pumps must overcome to provide water to the consumer:

Total Head = Static Head + Friction Head + Velocity Head (9.7)


The following examples are provided to increase your skill in solving practical calculations for pressure and head. Recall that:

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