> ## Content Index
> Fetch the complete content index at: https://www.machinerymatters.com/llms.txt
> Use this file to discover other available public pages before exploring further.

# Liquid Head: Pressure, Velocity, and Elevation Head
- URL: https://www.machinerymatters.com/liquid-head-pressure-velocity-and-elevation-head/
- Published: 2026-10-24T12:00:00.000Z
- Updated: 2026-10-28T10:57:08.000Z
- Description: Head is the mechanical energy of a liquid per unit weight, expressed as a height of the liquid. The static pressure of a flowing liquid and how a wall tap reads it, pressure head for any specific gravity, stagnation pressure, velocity head from the flow and the pipe bore, and elevation head.
- Author: Editor
- Tags: Fluid Mechanics, Article, #series-pressure-and-head

This is the second article [in a series](https://www.machinerymatters.com/pressure-and-head-series/) on the topics of pressure and head. This article covers:

- what head is,
- the static pressure of a flowing liquid,
- pressure head,
- stagnation pressure and velocity head, and
- elevation head.

## The Concept of Head

Head is the mechanical energy of a liquid per unit weight of the liquid. Energy per unit weight has the dimension of a length, since a foot-pound of energy per pound of liquid is a foot, and a joule per newton is a meter. A head is therefore expressed as a height of the liquid itself. A flowing liquid has three heads, one for each form of its mechanical energy:

- The pressure head *P*/*ρg* is the work that its pressure can do per unit weight, with *P* the static pressure, *ρ* the density of the liquid, and *g* the gravitational acceleration.
- The velocity head *v*²/2*g* is its kinetic energy per unit weight, with *v* the local velocity, the velocity of the liquid at one point of the pipe’s cross-section (Figure 1).
- The elevation head *z* is its potential energy per unit weight, the height of the liquid above a reference level called the datum.

Each head is found from quantities that can be measured: the pressure from a tap in the pipe wall, the mean velocity from the flow and the bore of the pipe, and the elevation from the layout of the piping.

Datum Wall tap Tube facing the flow v z P/ρg v²/2g 

**Figure 1.** The heads at a point in a pipe, shown by open tubes. The centerline lies at elevation *z* above the datum. At the wall tap, the liquid stands at the pressure head *P*/*ρg* above the centerline. *P* is the static pressure at the centerline. Across a straight pipe the static pressure varies only with elevation, as in a liquid at rest, so the wall tap at the top of the pipe gives this level. The velocity is zero at the wall and greatest near the center. In the tube facing the flow, the liquid stands higher by *v*²/2*g*, the velocity head of the liquid arriving at the tube’s open end.

## Static Pressure

The static pressure of a flowing liquid is the pressure that the liquid exerts on a surface moving with it. The name refers to the condition under which it would be measured. Relative to an instrument carried along with the liquid, the liquid appears static.

In a pipe, the static pressure is read through a pressure tap, a hole through the pipe wall that admits the pressure to a pressure indicator. The velocity of liquid flowing in a pipe is zero at the pipe’s wall and higher toward its center. Because the pipe’s wall and the liquid in contact with it move together, the pressure measured there is the static pressure.

Where the flow runs straight, the static pressure does not change between the wall and the stream beside it, so a tap in the wall reads the static pressure of the stream passing it. Downstream of an elbow, a valve, a reducer, or a tee, the flow may be uneven or may swirl. The static pressure then varies around the circumference of the pipe and across it. In such flow, a tap in the wall may not read the static pressure of the stream. Taps should therefore be placed on straight pipe, clear of such fittings. Where the piping allows, a tap should be placed no closer to the components upstream and downstream of it than the distances in Table 1\. Each distance is a length of straight pipe of the tap’s bore, from the end of the component to the centerline of the tap, given in multiples of the pipe’s inside diameter *D*. Figure 2 illustrates various tap locations to demonstrate the effect on a pressure indicator’s reading.

Upstream of a fitting, a valve, a strainer, or an orifice plate, the flow is disturbed only within about one pipe diameter of the component, so 2*D* suffices. Downstream of such a component, the distance grows with the disturbance.

For an accurate reading, the hole should be small, drilled perpendicular to the wall, flush with its inner surface, and free of burrs, so that it disturbs the flow as little as possible. A burr at the edge of the hole offsets the reading, as does a hole drilled at an angle to the wall.

| Component                                                                                                 | Tap upstream of the component | Tap downstream of the component |
| --------------------------------------------------------------------------------------------------------- | ----------------------------- | ------------------------------- |
| Long-radius elbow (centerline radius about 1.5*D*) or gentler bend                                        | 2*D*                          | 5*D*                            |
| Short-radius or mitered elbow                                                                             | 2*D*                          | 10*D*                           |
| Tee, flow passing straight through the run (branch closed, or drawing off part of the flow)               | 2*D*                          | 5*D*                            |
| Tee, flow turning through the branch, or joined by flow from the branch                                   | 2*D*                          | 10*D*                           |
| Concentric or eccentric reducer, narrowing or widening                                                    | 2*D*                          | 5*D*                            |
| Gate, ball, plug, or butterfly valve, fully open                                                          | 2*D*                          | 5*D*                            |
| Control valve, any valve partly closed, globe valve, angle valve, check valve, strainer, or orifice plate | 2*D*                          | 10*D*                           |
| Pump suction flange                                                                                       | 3*D*                          | —                               |
| Pump discharge flange\*                                                                                   | —                             | 2*D*                            |

**Table 1.** Minimum length of straight pipe between a pressure tap and a component upstream or downstream of it. *D* is the inside diameter of the pipe at the tap.

\* The volute is the spiral passage in the pump’s casing that leads the liquid to the discharge. It lies in a plane perpendicular to the pump’s shaft. The tap should be perpendicular to that plane, and so parallel to the shaft.

Downstream of a long-radius elbow Flow ≥ 5D ≥ 2D D Vertical pipe Flow Downstream of a control valve Flow < 10D Outer wall of a bend Flow Capped end of a tee Branch Flow 

**Figure 2.** Readings of pressure taps on pipes carrying liquid at the same flow and static pressure. The blue triangle on each indicator dial marks the static pressure of the stream where the flow runs straight. The dial needles are drawn to the right or left of the blue triangle to illustrate whether the indicator reading would tend to be high or low relative to the static pressure, but they should not be interpreted as precise representations of the magnitude of the difference. The tap downstream of the long-radius elbow is marked with a green check mark. It reads the static pressure of the stream. It is a small perpendicular hole, flush with the inner surface of the wall and free of burrs. It is on straight pipe, at least 5*D* downstream of the elbow and at least 2*D* upstream of the flange of the next fitting or valve. *D* is the inside diameter of the pipe. In the vertical pipe, the flow runs upward. A hole of the same kind in the pipe’s wall is also marked with a green check mark. It reads the static pressure of the stream at the hole’s elevation. A red X marks each of the other taps, none of which reads the static pressure of the stream. The tap downstream of the control valve is less than 10*D* from the valve. In the valve’s narrow opening, the liquid speeds up and its static pressure falls. Part of the fall in static pressure is recovered as the jet leaving the opening slows and spreads across the pipe. At the tap, the recovery is not yet complete. The tap therefore reads low. In the bend, the curvature of the flow raises the reading of the tap on the outer wall. In the tee, the flow turns into the branch. The liquid arriving at the capped end is brought nearly to rest. The indicator connected to the cap therefore reads high.

## Pressure Head

A column of liquid exerts a pressure at its base by its own weight, as described in [the article on pressure and its measurement](https://www.machinerymatters.com/pressure-and-its-measurement/). A pressure can therefore be expressed as the height of a column of the liquid whose weight would produce it at the column’s base. That height is the pressure head *h*p. In consistent SI units, the pressure head of a static pressure *P* in a liquid of density *ρ* is:

hp \= P / (ρ · g)

where:

- hp \= pressure head (m)
- P \= static pressure (Pa)
- ρ \= density of the liquid (kg/m³)
- g \= gravitational acceleration, 9.807 m/s²

Where the density of a liquid is given by its specific gravity *SG*, with the pressure in kPa and the pressure head in meters, the pressure head is:

hp \= 0.1020 · P / SG

where:

- hp \= pressure head (m)
- P \= static pressure (kPa)
- SG \= specific gravity of the liquid at its flowing temperature, relative to water at 39.2 °F (4 °C)

The constant 0.1020 is the reciprocal of 9.807, the pressure in kPa that a meter of water at 39.2 °F exerts at its base. With the pressure in bar, the constant is 10.20.

In US units, with the pressure in psi and the pressure head in feet, the pressure head is:

hp \= 2.307 · P / SG

where:

- hp \= pressure head (ft)
- P \= static pressure (psi)
- SG \= specific gravity of the liquid at its flowing temperature, relative to water at 39.2 °F (4 °C)

The constant 2.307 is 144 divided by 62.43\. These are the number of square inches in a square foot and the density of water at 39.2 °F in lb/ft³.

A pressure head differs from a manometric unit. A manometric unit such as the foot of water expresses a pressure as the height of a column of a reference liquid, so it remains a unit of pressure whatever liquid is present. A pressure head is a height of the liquid actually present, so it depends on that liquid’s density. A pressure of 7.37 psi is 17.00 ftH2O whatever the liquid, and it is 20.00 ft of head for a liquid having *SG* 0.85\. A pressure of 100 psi is 271 ft of head for a liquid having *SG* 0.85, and it is 210 ft of head for a liquid having *SG* 1.1.

## Stagnation Pressure and Velocity Head

A tube that projects into the stream with its open end facing the flow, as illustrated by the tube on the right side of Figure 1, reads a higher pressure than a wall tap at the same elevation. Liquid of density *ρ* arriving at the opening with the local velocity *v* is brought to rest there, and its kinetic energy is converted into pressure. The tube therefore reads the stagnation pressure *P*0, named for the stagnant liquid at its opening. In consistent SI units, the stagnation pressure exceeds the static pressure *P* by the kinetic energy of the arriving liquid per unit volume:

P0 \= P + ρ · v² / 2

where:

- P0 \= stagnation pressure (Pa)
- P \= static pressure (Pa)
- ρ \= density of the liquid (kg/m³)
- v \= local velocity of the liquid arriving at the open end of the tube (m/s)

Divided by *ρ*·*g*, the term *ρ*·*v*²/2 becomes *v*²/2*g*, the velocity head of the liquid arriving at the tube. In the open tubes of Figure 1, the liquid therefore stands higher in the tube facing the flow than in the tube at the wall tap by *v*²/2*g*. A tube of this kind is called a Pitot tube. It enables determination of the local velocity from the difference between the stagnation and static pressure readings.

Because the local velocity varies across the pipe, the velocity head *v*²/2*g* varies too. The mean velocity *V* is the volumetric flow divided by the flow area of the pipe. By convention, the velocity head *h*v of the flow in a pipe is calculated from the mean velocity:

hv \= V² / (2 · g)

where:

- hv \= velocity head (ft or m)
- V \= mean velocity (ft/s or m/s)
- g \= gravitational acceleration, 32.17 ft/s² or 9.807 m/s²

Flow in a pipe may be turbulent, with eddies that mix the liquid as it moves, or laminar, with the liquid moving in smooth layers that do not mix (Figure 3). Per unit weight of liquid, the kinetic energy that turbulent flow carries through a cross-section of the pipe is just a few percent above *V*²/2*g*, so the difference is usually neglected. Per unit weight of liquid, the kinetic energy that laminar flow carries through a cross-section of the pipe is roughly twice *V*²/2*g*, so it may require intentional accounting, depending on the circumstances.

Laminar flow V Turbulent flow V 

**Figure 3.** Laminar flow and turbulent flow in a pipe at the same mean velocity *V*. The lines at the left of each pipe trace paths of the liquid. In laminar flow the paths are straight and parallel. In turbulent flow they wander and cross, as eddies mix the liquid. The arrows at the right show the local velocity across the pipe. The dashed red line marks the mean velocity. The laminar profile is a parabola. At its center the velocity is twice the mean velocity. In turbulent flow the velocity rises steeply near the wall. At the center it is about 1.2 times the mean velocity.

In US units, with the flow *Q* in gpm and the pipe inside diameter *D* in inches, the mean velocity is:

V = 0.4085 · Q / D²

where:

- V \= mean velocity (ft/s)
- Q \= volumetric flow (gpm)
- D \= pipe inside diameter (in)

In SI units, with the flow in m³/h and the inside diameter in mm, it is:

V = 353.7 · Q / D²

where:

- V \= mean velocity (m/s)
- Q \= volumetric flow (m³/h)
- D \= pipe inside diameter (mm)

The velocity head depends on velocity alone, so in feet it is the same for every liquid. At 5, 10, and 15 ft/s it is 0.39, 1.55, and 3.50 ft, which for water at 39.2 °F corresponds to 0.17, 0.67, and 1.52 psi.

Units of flow, the determination of laminar or turbulent flow, and the continuity of flow through pipes of different bore will be covered in separate articles.

## Elevation Head

The elevation head is simply the altitude of the point in the liquid measured from the datum, a horizontal plane chosen for the calculation. Any horizontal plane may serve, provided that one datum is used for every elevation in the calculation. A point below the datum has a negative elevation head.

In a liquid at rest, the pressure at a point exceeds the pressure at a higher point by the weight, per unit area, of a column of the liquid whose height is the difference in their elevations. From a higher point to a lower one, the pressure head therefore rises by as much as the elevation head falls. For two points A and B in a continuous body of liquid at rest, at elevations *z*A and *z*B above the datum, where the pressures are *P*A and *P*B, the sum of the elevation head and the pressure head is the same at both. In consistent SI units, the relation is:

zA \+ PA / (ρ · g) = zB \+ PB / (ρ · g)

where:

- zA \= elevation of point A above the datum (m)
- PA \= pressure at point A (Pa)
- zB \= elevation of point B above the datum (m)
- PB \= pressure at point B (Pa)
- ρ \= density of the liquid (kg/m³)
- g \= gravitational acceleration, 9.807 m/s²

In an open tank of water at 39.2 °F whose surface is 20 ft above a datum at its base, the sum is 20 ft at every point, with the pressures taken as gauge (Figure 4). At the surface the gauge pressure is zero, and the sum is the elevation head of 20 ft. At the base the elevation head is zero, and the sum is the pressure head of 20 ft, a pressure of 8.67 psig. Halfway down, each head is 10 ft.

Water Datum A B C PA/ρg \= 10 ft zA \= 10 ft PB/ρg \= 0 ft zB \= 20 ft PC/ρg \= 20 ft zC \= 0 ft 

**Figure 4.** Elevation head and pressure head in an open tank of water at 39.2 °F whose surface is 20 ft above a datum at its base. Blue dots mark points A, B and C. Point A lies halfway down, at the bottom of the water column in the left tube, where *z*A and *P*A/*ρg* are each 10 ft. The dashed line marks the level of A, at which the pressure is *P*A in the tank and in both tubes. Point B lies on the surface, where *z*B is 20 ft and *P*B/*ρg* is zero. Point C lies on the datum, in the right tube, where *z*C is zero and *P*C/*ρg* is 20 ft. At each point the elevation head and the pressure head sum to 20 ft.

*Next in the series: [Total Dynamic Head](https://www.machinerymatters.com/total-dynamic-head/) — how to determine total head at a point and a pump’s total dynamic head, with a worked example.*