Introduction
Viscosity simply means friction in fluids.
It is observed that it is easier to pour water or kerosene from a container than to pour honey or engine oil. A little stone dropped into a cylinder of water gets to the bottom of the cylinder faster than when the same stone is dropped into a cylinder containing engine oil or glycerine, we can also draw inference from the time of movement of a teaspoonful of castor oil through your throat to that of a teaspoonful of water. These differences are due to the property of viscosity in these liquids.
Viscosity is the internal friction between layers of a liquid or gas in motion.
Liquids which pour slowly are said to be more viscous than those which pour faster. Hence very cold thick palm oil is more viscous than very cold water.
The movement of one layer of fluid over a neighboring layer is opposed by viscous forces.
Also when a stone or a ball bearing is thrown down a cylinder of a viscous fluid, the downward motion of the body is opposed by the viscosity of the liquid. The opposition to the movement of the stone is a function of the viscosity of the fluid and hence the slower it motion.
Viscosity is denoted by h, measured in Nsm-2 (SI Unit) and a vector quantity.
Thus, h = Force/ Area x velocity gradient.
Effects of Viscosity
- It is responsible for the different rates of flow of fluids.
- It affects motion of bodies in fluids.
Terminal Velocity
When a stone falls through a viscous fluid, it is subject to three forces: its weight (W) acting downwards, the upthrust (U) of the liquid on the stone acting upwards and the viscous force (V) opposing its motion. The viscous force acts opposite to the motion of the stone, i.e. upwards.
We can therefore write the equation of motion of the stone as W –V –U = ma
Where a is the acceleration of the stone through the liquid, and m is the mass of the stone. The viscous force V increases with the speed of the stone. So as the stone falls faster and faster through the liquid , the viscous force opposing the motion increases until at a maximum speed, the viscous drag, balances the downward force of the weight of stone. At this point the stone moves with constant velocity because its acceleration a is now zero. Hence our equation becomes
W –V – U = ma = 0
Or V = W – U
This constant velocity is termed the terminal velocity.
The terminal velocity is the maximum velocity an object (e.g. a spherical ball in a liquid) when the frictional (viscous) force due to the motion of the object becomes or is equal to the apparent weight of the object in the fluid where there is no longer net force on the object. Thus, the force with which the object now moves is called the Drag Force.
Experiment to determine the terminal velocity of an object falling through a viscous fluid
The experiment to determine the terminal velocity of an object e.g. steel falling through a viscous liquid, glycerine, is described below:
AIM: To determine the terminal velocity of a steel ball falling through a jar of glycerine.
APPARATUS: Glycerine, calibrated cylinder jar, spherical steel ball, spring or lever balance, stop-watch or clock and micro-meter screw-gauge.
METHOD: A small mass of a spherical steel ball is attached to a spring or level balance, which is then lowered into a cylindrical jar filled with glycerine nearly to the brim. The steel ball is then allowed to freely until it reaches its terminal or steady velocity.
The time taken to reach its terminal velocity is measured by the stopwatch or clock and the distance measured easily from the calibrated jar.
The diameter of the spherical steel ball is measured with the aid of the micro-meter screw-gauge, i.e. the radius of the spherical is obtained (2r = D).
OBSERVATION: It was observed that the object accelerated initially but after attaining its terminal velocity (constant) velocity, the steel – ball moves slowly in this velocity until it reaches the bottom of the jar.
PRECAUTION:
- Drop the ball gently.
- The ball must fall centrally down on the viscous liquid (glycerine)
- Avoid error of measurement, i.e. of mass, time, radius of the spherical ball.
EXERCISES
Lets see how much you’ve learnt, attach the following answers to the comment below
- Which of these is not correct for the equation of motion of the sphere? A. W –V –U = ma B. W –V – U = ma = 0 C. V = W + U D. V = W – U
- Examples of low viscous fluids are, except? A. Kerosene B. Engine oil C. Petrol D. Ethanol
- Examples of high viscous fluid are, except? A. Syrup B. Grease C. Glycerine D. Alcohol
- Viscous force (V) …………………………. the motion of the sphere. A. Supports B. Parallels C. Opposes D. None of the options correct.
- Viscosity is the internal between layers of a liquid or gas in motion. A. Support B. force C. velocity D friction
