# 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}, lb/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*, 62.4 l^{3}*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} * =

*, and (2) can be modified to*

*ρ*_{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*

*/ 60)*_{fpm}^{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*

#### 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

*- (2) can be simplified to*

*ρ*_{w}= 1000 kg/m^{3}*h _{w (m H2O)} = *

*((1.205 kg/m*^{3}) v^{2}*) /*(2*(**) 9.81 m/s**1000 kg/m*^{3}^{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.

*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 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 |