FLUID  PROPERTIES AND FORCES

CLASS NOTES FOR ENGINEERS 

 

Properties of a fluid plays an important role

in the study of fluid mechanics. There are

number of fluid forces acting.

Hydro-statics is the study of pressure of

a fluid at rest. When the fluid is at rest,

there are no shear stresses in the fluid.

Thus the pressure at a point on a plane

surface always acts normal to the surface.

There is no effect of viscous forces.

Pressure variation is only due to the weight

of the fluid. Consequently the analysis is

simple. It is analytically completely

analyzed. Hydro-statics means study of

pressure exerted by a liquid at rest. Fluid

pressure is always perpendicular to the

surface in contact.

TABLE: PROPERTIES OF FLUIDS, SYMBOL, DEFINITION, DIMENSION AND UNITS

Sr. No	PROPERTY	Sym- bol	Definition of Property	Dimensions	Units
1.	Mass Density	ρ	Mass per unit volume, m/V	ML-3	Kg/m3
2.	Weight Density	w	Weight per unit volume, w=W/V	ML-2T-2	N/m3
3.	Specific Volume	v	Volume per unit mass, v =V/m = 1/ρ	L3M-1	m3 / kg
4.	Specific Gavity	S	Density of substance / density of water	No units	————
5.	Dynamic Viscosity	μ	From Newton’s Law μ =τ/(du/dy),	ML-1T-1	Ns / m2
6.	Kinematic Viscosity	v	v = μ/ρ = Dynamic viscosity/ density	L2T-1	m2 / s
7.	Surface Tension	σ	Force per unit length at the free surface	MT-2	N/m
8.	Vapor Pressure	p	Vapor pressure p	ML-1T	N/m2

Predominant Forces in Fluid Mechanics

Forces in fluid  mechanics which control the motion of a fluid. Main fluids of interest are air and water. The following forces need significant attention while dealing with a stationary fluid or a flowing fluid.

1. Inertia force
It is always present in a flowing fluid. Inertia force = mass x acceleration.
It acts opposite to the direction of acceleration or de-acceleration. Unit of this force is N.

Fi = m x a

2. Gravity force
It is equal to mass x acceleration due to gravity. It acts vertically downwards. Unit of this force is N.

W = m x g

3. Viscous force
It is due to viscosity of the fluid. It is equal to the product of shear stress and surface area of flow. Unit of this force is N.

Fv = τ x A = (µdu/dy) x A

4. Surface tension
It is a tensile force. It is due to cohesion at the free surface of a fluid.
(Cohesion: Forces of attraction between molecules of the same substance). Free surface formation of a fluid is due to the surface tension. Surface tension has the symbol σ and is expressed as force per unit length (N/m).

F _st = σ x L

5. Pressure force
It is equal to the product of pressure and area normal to the pressure. It is in Newton.

F _p = p x A

6. Elastic force
It is product of elastic stress and area of flow.  Unit of this force is N.

F_e = σ x A

7. Buoyant force: force exerted on an immersed object due to the upward thrust. Unit of this force is N.

Buoyant force = Weight of the fluid displaced= Volume of object immersed in fluid x density of fluid x g

HYDRO-STATIC FORCES  ON SURFACES

TOTAL PRESSURE AND CENTER OF

PRESSURE

Total pressure means resultant force on the body in contact with a liquid. Center of pressure means the location of point of resultant force with respect to the free surface of the liquid.

Let F = p x A be the total pressure force
‘y’ is the location of the center of pressure from the free surface of the liquid
Various submerged surfaces are
(i) HORIZONTALLY IMMERSED SURFACE

Pressure will be same everywhere since every point of the surface is at equal distance from the free surface.
P = ρgy A

(ii) VERTICAL SUBMERGED SURFACE

PRESSURE CHANGES WITH DEPTH

Force P = ρgy₁ A
Where y₁ is the DISTANCE OF CENTER OF GRAVITY of the body from the free surface of the liquid

Location of Center of pressure =y = I / A y₁
Where I is the moment of inertia of the body about the free surface of the liquid
I = I_G + A y₁²

where  G is center of gravity of the submerged surface

A is the surface area of the body in contact with the liquid

y₁ is the distance of center of gravity of the body from the free

surface of the liquid

Location of center of pressure

It is a single point where the resultant force acts.

y= ( I_G + A y₁²)/ (Ay₁) = (I_G / Ay₁ )+ y₁

(iii) INCLINED SUBMERGED SURFACE

Let θ the angle made by the top plane surface with the free surface of the liquid.

y is the distance along the top surface

x is the distance perpendicular to the top surface

h is the depth of a point from the free surface
P = ρg y₁ A
y = (I_G sin2θ/Ay₁) + y₁

 

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