# 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*, and (2) can be modified to

_{ w }* 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*- (2) can be simplified to

_{w }= 1000 kg/m^{3}* 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.

## Related Documents

### 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.