### Fluid Pressure Formula:

Fluid pressure formula P_{fluid(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 meter^{3} 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

P_{fluid(pa) } = P _{(N/m2)}+ρ _{(kg /m3)}* g_{(m/s)}* h_{(m)}

Where

P= pressure at the reference point

P_{fluid } = 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

P_{fluid } = P +ρ_{0} * g* h

Where

ρ_{0} = 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 /m^{3}.

### Answer:

H_{1}=40m

H_{2} =80 m

Ρ =200 kg /m^{3}

P_{fluid } = 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 =8cm^{2} = 8*10^{-4} m^{2}

ρ = 1 g/cm^{3} =1000 kg /m^{3}

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