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/ft²))

ρ_f = 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 (lb_f /ft²) = 47.88 N/m²(Pa) = 0.006944 lb_f /in²(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 v²) / ( ρ_w g)

= ρ_f v²/ (2 ρ_w g)                  (2)

where

h_w = head water (m Water, ft Water)

γ_w = ρ_w g = specific weight water (9807 N/m³, 62.4 l b_f /ft³ )

where

ρ_w = 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 ρ_f = ρ_w , and (2) can be modified to

h_w = v²/ 2 g             (3)

Or simplified to

Metric Units

h_{w (m H2O)} = 0.051 v²            (3b)

h_{w (mm H2O)} = 51 v²            (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/m³ (20 ^oC) and the reference fluid is water with ρ_w = 1000 kg/m³ - (2) can be simplified to

h_{w (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

h_{w (mm H2O)} = 6.1 10^-2 v²              (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 ^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 .

head

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 and Dynamic Head Chart (pdf)

Air Flow - Velocity Heads

Table based on ρ_f = 1.205 kg/m³ (C = 4005, temperature 70 ^oF) and ρ_w = 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