# Dynamic Pressure

## Dynamic pressure is the kinetic energy per unit volume of a fluid

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Dynamic pressure is the kinetic energy of a flowing fluid - liquid or gas - per unit volume - and can be expressed as

p_{d}= 1/2 ρ v^{2}(1)

where

p_{d }= dynamic pressure (N/m^{2}(Pa), lb_{f}/ft^{2}(psf))

ρ = density of fluid (kg/m^{3}, slugs)

v = velocity (m/s, ft/s)

### Dynamic Pressure Calculator - SI Units

The default values below are for water with density of *1000 kg/m ^{3}*.

*ρ - density of fluid (kg/m ^{3})*

*v - velocity (m/s) *

*1 N/m*^{2}= 1 Pa = 1.4504x10^{-4}lb_{f}/in^{2}(psi) = 0.02089 lb_{f}/ft^{2}(psf) = 1x10^{-5}bar = 4.03x10^{-3}in water = 0.336x10^{-3}ft water = 0.1024 mm water = 0.295x10^{-3}in mercury = 7.55x10^{-3}mm mercury = 0.1024 kp/m^{2}= 0.993x10^{-5}atm

### Dynamic Pressure Calculator - Imperial Units

The default values below are for water with density of *1.940 slugs*.

*ρ - density of fluid ( slugs)*

*v - velocity (ft/s) *

Some common densities at atmospheric pressure:

- Water -
*0*^{o}C - 1000 kg/m^{3} - Water -
*32*^{o}F -*1.940 slugs/ft*^{3} - Air -
*20*^{o}C - 1.2 kg/m^{3} - Air -
*60*^{o}F -*2.373 10*^{-3}slugs/ft^{3}

### Example - The Dynamic Pressure in a Water Flow

The dynamic pressure in water with - temperature *20 ^{o}C* - density

*1000 kg/m*and velocity

^{3}*5 m/s*- can be calculated as

p_{d}= 1/2 (1000 kg/m^{3}) (5 m/s)^{2}

= 12500 Pa

= 12.5 kPa

### Example - The Force acting on a Wall from a Hurricane

The dynamic pressure in a hurricane with air temperature *20 ^{o}C,* density of air

*1.2 kg/m*and wind velocity

^{3}*37 m/s*can be calculated as

p_{d}= 1/2 (1.2 kg/m^{3}) (37 m/s)^{2}

= 821 Pa (N/m^{2})

The force acting directly on a wall with area *10 m ^{2} *can be calculated as

*F = p _{d} A *

* = (821 N/m ^{2}) (10 m^{2})*

* = 8210 N*

* = 8.2 kN*

* *- almost the weight of a small car.

Note that the real force acting on the wall - or an other obstruction in the wind - in general is more complicated to calculate than this due to drag and other effects.

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