Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

Head ( $$h$$ ) is used to express pressure or pressure energy.

Static head ( $$h_s$$) is the distance from the centerline of the gauge and above, to the surface of the liquid or you could say the difference in elevation.  The gauge in the pipe measures the pressure created by the weight of the liquid that is above the centerline of the gauge.

The gauge measures the static pressure of the static head.  The static preasure is less than the static head because of the loss of fluid friction and head velocity which the gauge can not measure.

## Head Friction loss in fittings and valves

This formula calculates the loss of head in a valve or fitting.

### Head Friction loss in fittings and Valves Formula

$$\large{ h_f = K \frac { v_{a}{^2} } { 2g } }$$

Where:

$$\large{ h_f }$$ = head frictional resistance (ft)

$$\large{ g }$$ = gravitational acceleration  (32.2 feet per second/per second)

$$\large{ v_a }$$ = average velocity in the pipe (ft/sec)

$$\large{ K }$$ = resistance coefficient for fittings or valves

## Resistance Coefficient

### Resistance Coefficient Formula

$$\large{ K = f \frac{L}{d_i} }$$

Where:

$$\large{ K }$$ = resistance coefficient

$$\large{ d_i }$$ = internal diameter

$$\large{ f }$$ = friction factor

$$\large{ L }$$ = equivalent length

$$\large{ h = \frac { 2.31 \;\;x\;\; p } { SG } }$$

$$\large{ p = \frac { h\;\;x\;\; SG } { 2.31 } }$$

Where:

$$\large{ h }$$ = head or height

$$\large{ p }$$ = pressure

$$\large{ SG }$$ = specific gravity

$$\large{ 2.31 }$$ = conversion factor (2.31 feet of fresh water = 1 psi)

Head velocity is when the liquid is allowed to flow from the tank while additional liquid is being added.  The movement of the liquid through the pipe is converted to kinetic energy that is called head velocity.

$$\large{ \Delta h = \frac{u^2}{2g} }$$

Where:

$$\large{ \Delta h }$$ = head loss of flowing fluid

$$\large{ g }$$ = gravitational acceleration  (32.2 feet per second/per second)

$$\large{ u }$$ = fluid velocity

Static suction is the height of the liquid surface in the suction tank above the centerline of the pump.

Static discharge is the highest liquid surface in the discharge system above the centerline of the pump.

$$\large{ H = h_d \;-\; h_s }$$

Where:

$$\large{ H }$$ = system head

$$\large{ h_d }$$ = total discharge head

$$\large{ h_s }$$ = total suction head

Total head is the sum of the discharge flange and the sum of the suction flange.

$$\large{ h_t = \left( h_{dg} + h_{dv} \right) \;-\; \left( h_{sg} + h_{sv} \right) }$$

Where:

$$\large{ h_t }$$ = total head or height

$$\large{ h_{dg} }$$ = discharge gauge head

$$\large{ h_{dv} }$$ = discharge velocity head

$$\large{ h_{sg} }$$ = suction gauge head

$$\large{ h_{sv} }$$ = suction velocity head

$$\large{ h_d = h_{sd} + h_{pd} + h_{fd} }$$

Where:

$$\large{ h_d }$$ = total discharge head

$$\large{ h_{sd} }$$ = static discharge head

$$\large{ h_{fd} }$$ = friction discharge head

$$\large{ h_{pd} }$$ = surface discharge pressure

$$\large{ h_s = h_{ss} + h_{ps} + h_{fs} }$$

Where:

$$\large{ h_s }$$ = total suction head

$$\large{ h_{ss} }$$ = static suction head

$$\large{ h_{fs} }$$ = friction suction head

$$\large{ h_{ps} }$$ = surface suction pressure