Velocity Pressure Head
Dynamic pressure or velocity head.
The dynamic pressure in a fluid flow can be expressed as
p _{ d } = 1/2 ρ _{ f } v ^{ 2 } (1)
where
p _{ d } = dynamic pressure in fluid (Pa, ps _{ f } (lb/ft ^{ 2 } ))
ρ _{ f } = density of fluid (kg/m ^{ 3 } , slugs /ft ^{ 3 } )
v = fluid velocity (m/s, ft/s)
 1 Pa = 10 ^{ 6 } N/mm ^{ 2 } = 10 ^{ 5 } bar = 0.1020 kp/m ^{ 2 } = 1.02x10 ^{ 4 } m H _{ 2 } O = 9.869x10 ^{ 6 } atm = 1.45x10 ^{ 4 } psi (lbf/in ^{ 2 } )
 1 psf (lb _{ f } /ft ^{ 2 } ) = 47.88 N/m ^{ 2 } (Pa) = 0.006944 lb _{ f } /in ^{ 2 } (psi)
Head loss as water column can be calculated by dividing the dynamic pressure with the specific weight of water like
h _{ w } = p _{ d } / γ _{ w }
= ( 1/2 ρ _{ f } v ^{ 2 } ) / ( ρ _{ w } g)
= ρ _{ f } v ^{ 2 } / (2 ρ _{ w } g) (2)
where
h _{ w } = head water (m Water, ft Water)
γ _{ w } = ρ _{ w } g = specific weight water (9807 N/m ^{ 3 } , 62.4 l b _{ f } /ft ^{ 3 } )
where
ρ _{ w } = density of water (1000 kg/m ^{ 3 } , 1.940 slugs/ft ^{ 3 } )
g = acceleration of gravity ( 9.81 m/s ^{ 2 } , 32.174 ft/s ^{ 2 } )
Water Flow
If the flowing fluid is water  then ρ _{ f } = ρ _{ w } , and (2) can be modified to
h _{ w } = v ^{ 2 } / 2 g (3)
Or simplified to
Metric Units
h _{ w } _{ (m H2O) } = 0.051 v ^{ 2 } (3b)
h _{ w } _{ (mm H2O) } = 51 v ^{ 2 } (3c)
where
v = velocity (m/s)
Imperial Units
h _{ w } _{ (ft H2O) } = 0.0155 v _{ fps } ^{ 2 } (3d)
h _{ w } _{ (in H2O) } = 0.186 v _{ fps } ^{ 2 } (3e)
where
v _{ fps } = velocity (ft/s)
or
h _{ w } _{ (ft H2O) } = 0.0155 (v _{ fpm } / 60) ^{ 2 } (3f)
h _{ w } _{ (in H2O) } = 0.186 (v _{ fpm } / 60) ^{ 2 } (3g)
where
v _{ fpm } = 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
Water Flow Velocity  v  (ft/sec)  Velocity Head  h _{ w }  (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 ρ _{ f } = 1.205 kg/m ^{ 3 } (20 ^{ o } C) and the reference fluid is water with ρ _{ w } = 1000 kg/m ^{ 3 }  (2) can be simplified to
h _{ w (m H2O) } = ((1.205 kg/m ^{ 3 } ) v ^{ 2 } ) / (2 ( 1000 kg/m ^{ 3 } ) 9.81 m/s ^{ 2 } )
= 6.1 10 ^{ 5 } v ^{ 2 } (4)
where
v = air velocity (m/s)
or
h _{ w (mm H2O) } = 6.1 10 ^{ 2 } v ^{ 2 } (4b)
Note!  these simplified equations must be relaculated for other air temperatures and densities .
Imperial Units
h _{ w } _{ (ft H2O) } = (v / C) ^{ 2 } / 12 (4c)
h _{ w } _{ (in H2O) } = (v / C) ^{ 2 } (4c)
where
v = velocity (ft/min)
C = constant (4005 for temperature 70 ^{ o } F)
The constant C and temperature:
Air Temperature ( ^{ o } F) 
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/m ^{ 3 } and water density 1000 kg/m ^{ 3 } .
Air Flow  Velocity Heads
Table based on ρ _{ f } = 1.205 kg/m ^{ 3 } (C = 4005, temperature 70 ^{ o } F) and ρ _{ w } = 1000 kg/m ^{ 3 } ( 1.940 slugs/ft ^{ 3 } ) .
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 
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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