Velocity Pressure 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 .

head

mm H2O

in H2O

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Water Flow - Velocity and Dynamic Head Chart

• Water Flow - Velocity and Dynamic Head Chart (pdf)

Water Flow - Velocity Heads

• 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:

Constant C vs. Air Temperatures

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 .

head

mm H2O

in H2O

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 and Dynamic Head Chart (pdf)

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 ) .

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

Temperature ^oC
K
^oF

Length m
km
in
ft
yards
miles
naut miles

Area m²
km²
in²
ft²
miles²
acres

Volume m³
liters
in³
ft³
us gal

Weight kg_f
N
lbf

Velocity m/s
km/h
ft/min
ft/s
mph
knots

Pressure Pa
bar
mm H₂O
kg/cm²
psi
inches H₂O

Flow m³/s
m³/h
US gpm
cfm