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Fluid Statics

Fluid Statics

The word “statics” is derived from Greek word

“statikos”= motionless

 For a fluid at rest or moving in such a manner that

there is no relative motion between particles there

are no shearing forces present:

Rigid body approximation

Pascal’s Laws

 Pascals’ laws:

• Pressure acts uniformly in all directions on a

small volume (point) of a fluid

• In a fluid confined by solid boundaries, pressure

acts perpendicular to the boundary – it is a

normal force.

Direction of fluid pressure on boundaries

Furnace duct Pipe or tube Heat exchanger

Dam

Pressure is a Normal Force (acts perpendicular to surfaces) It is also called a Surface Force

Units for Pressure

Unit Definition or Relationship

1 pascal (Pa) 1 kg m-1^ s-

1 bar 1 x 10^5 Pa

1 atmosphere (atm) 101,325 Pa

1 torr 1 / 760 atm

760 mm Hg 1 atm

14.696 pounds per

sq. in. (psi)

1 atm

Measurement of Pressure

Mechanical and electronic pressure measuring devices:

When a pressure acts on an elastic structure it will deform. This

deformation can be related to the magnitude of the pressure.

• Bourdon pressure gage

Pressure transducers convert pressure into an electrical output

Strain-gage pressure transducers are suitable for rapid changes in

pressure and cover big ranges of pressure values

  S  mgzg

PS z

x

y

Let Pz and Pz+z denote the z

pressures at the base and

top of the cube, where the

elevations are z and z+z

respectively.

What are the z-direction forces?

PS (^) z  z

Pressure distribution for a fluid at rest

 Fz^ ^0  PS z  PS z  z ^  S  zg

g z

Pz (^) z Pz    

 

g dz

dP   

A force balance in the z direction gives:

For an infinitesimal element (z0)

Pascal’s principle (The hydrostatic paradox)

• The pressure in a homogeneous, incompressible fluid at rest depends on the depth of the fluid relative to some reference plane, and it is not influenced by the size or shape of the tank or container Fluid is the same in all containers

Pressure is the same at the bottom of all containers

h

Vertical plane surfaces

The lock gate of a canal is rectangular, 20 m wide and 10 m high.

One side is exposed to the atmosphere and the other side to the water. What is the net force on the lock gate?

F

Vertical rectangular wall (wall width = W)

H

h Here the pressure varies linearly with depth: P=gh

P

Buoyancy

• A body immersed in a fluid experiences a vertical buoyant force equal to the weight of the fluid it displaces
• A floating body displaces its own weight in the fluid in which it floats Free liquid surface

The upper surface of the body is subjected to a smaller force than the lower surface

 A net force is acting upwards

F 1

F 2

h 1

h 2

H

Buoyancy

The net force due to pressure in the vertical direction is:

FB = F 2 - F 1 = (Pbottom - Ptop) (xy)

The pressure difference is:

Pbottom – Ptop =  g (h 2 -h 1 ) =  g H

Combining:

FB =  g H (xy)

Thus the buoyant force is:

FB =  g V

Measurement of Pressure

Manometers are devices in which one or more

columns of a liquid are used to determine the

pressure difference between two points.

• U-tube manometer
• Inclined-tube manometer

Measurement of Pressure Differences

b b m a m

a b m m P P g Z gR

P P g Z R  

   

   ( )

( )

3

2

Pa  Pb  gRm (   a  b )

Apply the basic equation of static fluids to both legs of manometer, realizing that P 2 =P 3.