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Velocity Pressure Head

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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, slugs/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


Water Flow - Velocity and Dynamic Head Chart

Water Flow - Velocity Heads 

Velocity Heads vs. water Flow Velocities
Water Flow Velocity
- v -
(ft/sec)



Velocity Head
- 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:

Constant C vs. Air Temperatures
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


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).

Velocity Heads vs. Air Flow Velocities
Air Flow Velocity
- v -
(ft/sec)



Velocity Head
- 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
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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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Dynamic Pressure

Dynamic pressure is the kinetic energy per unit volume of a fluid in movement.

Pipe and Duct Systems - Total Head Loss

Major and minor loss in pipes, tubes and duct systems.

Pipe Line Velocities vs. Fluid

Typical fluid flow velocities for common liquids, gases and vapors.

Pitot Tubes

Pitot tubes can be used to measure fluid flow velocities by measuring the difference between static and dynamic pressure in the flow.

Static Pressure vs. Head

Static pressure vs. pressure head in fluids.

Velocity-Area Flowmetering

Flow rate or discharge in an open conduit, channel or river can be calculated with the velocity-area principle.

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