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## Dynamic pressure or velocity head.

The dynamic pressure in a fluid flow can be expressed as

pd1/2 ρf v2                                       (1)

where

pd = dynamic pressure in fluid (Pa, psf (lb/ft2))

ρf = density of fluid (kg/m3, lb/ft3)

v = fluid velocity (m/s, ft/s)

• 1 Pa = 10-6 N/mm2 = 10-5 bar = 0.1020 kp/m2 = 1.02x10-4 m H2O = 9.869x10-6 atm = 1.45x10-4 psi (lbf/in2)
• 1 psf (lbf/ft2) = 47.88 N/m2 (Pa) = 0.006944 lbf/in2 (psi)

Head loss as water column can be calculated by dividing the dynamic pressure with the specific weight of water like

hw = pγw

= (1/2  ρf v2) / (ρw g)

=   ρf v2 / (2 ρw g)                 (2)

where

hw = head water (m Water, ft Water)

γw  = ρw g = specific weight water (9807 N/m3, 62.4 lbf/ft3)

where

ρw = density of water (1000 kg/m3, 1.940 slugs/ft3)

g = acceleration of gravity (9.81 m/s2, 32.174 ft/s2)

### Water Flow

If the flowing fluid is water - then ρf ρw , and (2) can be modified to

hw = v2/ 2 g                                             (3)

Or simplified to

#### Metric Units

hw (m H2O) = 0.051 v2                                    (3b)

hw (mm H2O) = 51 v2                                    (3c)

where

v = velocity (m/s)

#### Imperial Units

hw (ft H2O) = 0.0155 vfps2                                    (3d)

hw (in H2O) = 0.186 vfps2                                    (3e)

where

vfps = velocity (ft/s)

or

hw (ft H2O) = 0.0155 (vfpm / 60)2                                    (3f)

hw (in H2O) = 0.186 (vfpm / 60)2                                    (3g)

where

vfpm = velocity (ft/min)

#### Water Flow - Head to Velocity Calculator

This calculator can be used to calculate water velocity in a pipe or water stream from a measured head of water column. The dynamic pressure as head is typically measured with a pitot tube

mm H2O

in H2O

#### Water Flow - Velocity and Dynamic Head Chart #### Water Flow - Velocity Heads

Water Flow Velocity
- v -
(ft/sec)

- hw -
(ft H2O)

0.5 0.004
1.0 0.016
1.5 0.035
2.0 0.062
2.5 0.097
3.0 0.140
3.5 0.190
4.0 0.248
4.5 0.314
5.0 0.389
5.5 0.470
6.0 0.560
6.5 0.657
7.0 0.762
7.5 0.875
8.0 0.995
8.5 1.123
9.0 1.259
9.5 1.403
10.0 1.555
11.0 1.881
12.0 2.239
13.0 2.627
14.0 3.047
15.0 3.498
16.0 3.980
17.0 4.493
18.0 5.037
19.0 5.613
20.0 6.219
21.0 6.856
22.0 7.525
• 1 ft (foot) = 0.3048 m = 12 inches = 0.3333 yd

### Air Flow

#### Metric Units

If the flowing fluid is air with ρf = 1.205 kg/m3 (20oC) and the reference fluid is water with ρw = 1000 kg/m3 - (2) can be simplified to

hw (m H2O) ((1.205 kg/m3) v2) / (2 (1000 kg/m3) 9.81 m/s2)

= 6.1 10-5  v2                        (4)

where

v = air velocity (m/s)

or

hw (mm H2O) = 6.1 10-2  v2                        (4b)

Note! - these simplified equations must be relaculated for other air temperatures and densities

#### Imperial Units

hw (ft H2O) = (v / C)2 / 12                                   (4c)

hw (in H2O) = (v / C)2                                    (4c)

where

v = velocity (ft/min)

C = constant (4005 for temperature 70 oF)

The constant C and temperature:

 Air Temperature(oF) C 35 3872 40 3891 45 3910 50 3932 55 3952 60 3970 65 3987 70 4005 75 4025 80 4045 85 4064 90 4081 95 4101 100 4117 150 4298

#### Air Flow - Head to Velocity Calculator

This calculator can be used to calculate air velocity in a duct or air stream from a measured head of water column. The dynamic pressure as head is typically measured with a pitot tube

mm H2O

in H2O

#### Velocity and Dynamic Head Chart

Charts are based on air density 1.205 kg/m3 and water density 1000 kg/m3. #### Air Flow - Velocity Heads

Table based on ρf = 1.205 kg/m3 (C = 4005, temperature 70oF) and ρw = 1000 kg/m3 (1.940 slugs/ft3).

Air Flow Velocity
- v -
(ft/sec)

- hw -
(ft H2O)

5 0.00047
10 0.0019
15 0.0042
20 0.0075
25 0.012
30 0.017
35 0.023
40 0.030
45 0.038
50 0.047
55 0.057
60 0.067
65 0.079
70 0.092
75 0.11
80 0.12
85 0.14
90 0.15
95 0.17
100 0.19

## Related Topics

• Fluid Mechanics - The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

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## Citation

• Engineering ToolBox, (2005). Velocity Pressure Head. [online] Available at: https://www.engineeringtoolbox.com/velocity-head-d_916.html [Accessed Day Mo. Year].

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