FE Physics
Formulas & Explanation     Fluids

Under pressure we mean the force per unit area

Units of pressure are:  Nm -2 , Pa (scal) and  bar

1 Nm-2  = 1 Pa

1 bar = 1.0 x 105 N m -2

p = F/A

F  force in  N

A  area in m2

Hydrostatic pressure or fluid pressure

The hydrostatic pressure of a column of liquid :

p = ρgh

ρ  density of the fluid in kg m-3

g   gravitational acceleration in ms-2

h   height of the column fluid in m

Example

a.           Calculate the pressure of water at a depth of 70 m.

p=  ρgh = (1.00 x 103 )(9,81) (70) = 6.87 x 105  Pa

b.       Calculate the total pressure p’ at a depth of 70 m

p’ = p + pA  = 6.87 x 105  + 1.0 x 105 = 7.87 x 105 Pa

pA  atmospheric pressure

c.         Calculation of the total force F’ on a area of 1.00 km2  at a depth of 70 m

F’ = p’A = (7.87 x 105 )(1.0.106 )= 7.87 x 1011  N

( A in m2)

Law of continuity

Flow in a tube with different cross-sectional areas

v1 A1 = v2 A2

v1 speed of fluid at position 1                       v2 speed of fluid at position 2

A1 cross-sectional  area at position 1          A2 cross-sectional  area at position 2 So the speed of the flowing fluid is inversely proportional  to the cross-sectional area.