Mechanics of fluids-part-IV : Mechanics of fluids-part-IV By R.Buvana
Mechanics of fluids Part-IV : Mechanics of fluids Part-IV 1. Viscosity
2.Coefficient of viscosity
3.Stoke’s law
4.Streamline flow and turbulent flow
5..Force required to maintain laminar flow
6.Equation of continuity
7.energy of liquid
8.Bernoulli’s theorem
9.Application of Bernoulli’s theorem
Viscosity : Viscosity The property of a liquid by virtue of which an opposing force comes into play between different layers of a liquid whenever there is a relative motion between these layers of the liquid is called viscosity.
Coefficient of viscosity : Coefficient of viscosity F a A dv/dx
F=-?A dv/dx
F=?
F=viscous drag or back ward force
A=Area
Dv/dx=velocity gradient
Coefficient of viscosity=?
Thus, coefficient of viscosity of a liquid is defined as the viscous drag or force acting per unit area of the layer having unit velocity gradient perpendicular to the direction of the flow of the liquid.
Units of coefficient of viscosity : Units of coefficient of viscosity 1 poise=1dyne s/cm²
1decapoise=1 N s /m²
1decapoise= 1N s /m²
=10 5 dyne x1s /(10²cm)²
1decapoise= 10 poise
Stoke’s Law : Stoke’s Law Stoke’s proved that the viscous drag acting on a spherical body of radius r moving with terminal velocity v in a fluid of coefficient of viscosity ? is given by
F= 6 ? ? r v
Expression for terminal velocity : Expression for terminal velocity When a body is dropped in a viscous fluid, it is first accelerated and then its acceleration becomes zero and it attains a constant velocity called terminal velocity.
Conti… : Conti… The various forces acting on the body falling through the fluid are
(i)its weight(W) in the downward direction
(ii) upward thrust (T) equal to the weight of the displaced fluid
(iii) the viscous force (F) in a direction opposite to the direction of motion of the body.
Net downward force acting on the body=W-T-F
F=W-T
Conti… : Conti… W=4/3?r³?g
F= 6 ? ? r v
T=4/3?sr³
6 ? ? r v=4/3?r³?g-4/3?sr³
V=2/9r²(?-s)g/?
Which is the expression for the terminal velocity. The rain drops, parachute etc.fall with terminal velocity
Stream-line and Turbulent flow : Stream-line and Turbulent flow Stream line flow-When the flow of fluid is such that the velocity(v) of every particle at any point of the fluid is constant, then the flow is said to be steady or streamline flow.
Laminar Flow-If the liquid flows over a horizontal surface in the form of layers of different velocities, then the flow of liquid is called laminar flow.
Turbulent flow-The flow of fluid in which velocity of all particles crossing a given point is not same and the motion of the fluid becomes disorderly or irregular is called turbulent flow.
Force required to maintain laminar or streamline flow : Force required to maintain laminar or streamline flow According to Poiseuille’s equation , the volume of liquid flowing per unit time through a capillary tube of length l and radius r is given by
V=?Pr4/8?l
P=F/A
F=8 ? V l/ r²
Equation of continuity : Equation of continuity The equation of continuity expresses the law of conservation of mass in fluid dynamics.
a1 v1= a2v2 =m/?
Constant=av
This is called equation continuity and states that as the area of cross-section of the tube becomes larger, the fluid speed becomes smaller and vice –versa.
Home work questions : Home work questions 1.Why do clouds float in the sky?
2.Why a hot liquid moves faster than a cold liquid?
3.The accumulation of snow on the wings of an aeroplane reduces the lift.Why?