Fluid Pressure , Formula, Calculation with Example

Fluid Pressure Formula:

Fluid pressure formula Pfluid(pa)  in pascal is equal to the pressure at the reference point P (N/m2) in Newton per meter and addition the fluid’s density ρ (kg /m3) in kilogram per meter3 and multiply the acceleration because of gravity g(m/s) in meter per second and multiply the height from the reference point h(m) in meter.Hence the Fluid pressure formula can be written as

Pfluid(pa)  = P (N/m2)(kg /m3)* g(m/s)* h(m)

Where

P= pressure at the reference point

Pfluid   =  pressure at a point in a fluid

ρ =  fluid’s density

g =  acceleration because of gravity (considering earth g =9.8 m/s)

h= height from the reference point

The calculation of the density of the fluid can take place by dividing the fluid’s mass in consideration with the volume of fluid taken

ρ = m /v

where

m=  fluid’s mass

V= fluid’s volume considered

If the fluid is subject to atmospheric pressure, then the total pressure on the system is as

Pfluid  = P +ρ0 * g* h

Where

ρ0 = atmospheric pressure

Example:1

Calculate the change in pressure acting on the person(Fluid pressure)? In a person dives from a depth of 40m to a depth of 80m.Given the density of water is 200kg /m3.

Answer:

H1=40m

H2 =80 m

Ρ =200 kg /m3

Pfluid  = ρ * g* h

=2000*9.8*40

=784000 pa

For h =80 m

H=2000*9.8*80

H=156800 pa

Change in pressure =784000-156800 =627200 pa

Example:2

Calculate the force of water that acts on the fish? Acceleration due to gravity is 20N/Kg. The surface area of fish pressed by the water above is 8cm^2/) .

Answer:

G=20 N/kg

A =8cm2 = 8*10-4 m2

ρ = 1 g/cm3 =1000 kg /m3

Height of water =100-15 =85cm =85*10-2 m

P=F/A

F=P*A

= ρ *g*h*A

=2000*20*85*10-2*8*10-4

=27.2 N

Leave a Comment