Fluid at Rest and in Motion

Physics SSS1 Third Term

WEEK 2

Fluid at Rest and in Motion

Performance Objectives

Students should be able to:

1. Define Surface Tension, its effects and application
2. Explain capillary, cohesion, Adhesion, Viscosity
3. Define Terminal velocity and list applications of viscosity

Content

We observe many things in our day-to-day life. The surface Tension Phenomenon is one among them.   Often we confuse the Phenomena of Surface tension with Buoyancy. Both the phenomena are entirely different to each other in the sense, in Buoyancy a portion of the body gets dipped in the liquid whereas in Surface tension the body will be remaining on the layer of water without getting wet.
Let us observe these leaves on the surface of the water. We could see them moving in the water without getting wet.

For these leaves to be on the layer there should be some force acted by the upward layer of water which keeps the leaf on the surface. This is nothing but the Surface tension. Let us study more about the Surface tension in this section.

What is Surface Tension?

The Surface tension is defined as The dragging force observed in the given liquid per unit length. It is given by the formula:

T = FL

Where,
F = Force per unit length
L = Length over which the force acts.

The Surface tension is expressed in Newton per meter. 

What causes Surface Tension?

Surface tension is a physical property of water. Here the cohesive force keeps the water intact. Each molecule in the beaker is pulled in every direction equally by adjacent molecules.

Effects of Surface Tension

Several effects of surface tension can be seen with ordinary water:

1. Beading of rainwater on a waxy surface, such as a leaf. Water adheres weakly to wax and strongly to itself, so water clusters into drops. Surface tension gives them their near-spherical shape because a sphere has the smallest possible surface area to volume ratio.
2. The formation of drops occurs when a mass of liquid is stretched. The animation shows water adhering to the faucet gaining mass until it is stretched to a point where the surface tension can no longer bind it to the faucet. It then separates and surface tension forms the drop into a sphere. If a stream of water was running from the faucet, the stream would break up into drops during its fall. Gravity stretches the stream, and then surface tension pinches it into spheres.
3. Flotation of objects denser than water occurs when the object is non-wettable and its weight is small enough to be borne by the forces arising from surface tension. For example, water striders use surface tension to walk on the surface of a pond. The surface of the water behaves like an elastic film: the insect’s feet cause indentations in the water’s surface, increasing its surface area.
4. Separation of oil and water (in this case, water and liquid wax) is caused by a tension in the surface between dissimilar liquids. This type of surface tension is called “interface tension”, but its chemistry is the same.
5. Tears of wine are the formation of drops and rivulets on the side of a glass containing an alcoholic beverage. Its cause is a complex interaction between the differing surface tensions of water and ethanol; it is induced by a combination of surface tension modification of water by ethanol together with ethanol evaporating faster than water.

Surface tension Formula

The Surface tension is expressed by the formula:

T = FL

Where F = Force per unit length and
L = Length over which the force acts.

To calculate the tension we use the formula:

T = 12 ρ grh.

where h = h + r3.
Here
r = radius of the capillary tube at the liquid meniscus
h = height of the liquid in the capillary tube above the free surface of liquid in beaker.
ρ = Density of water (ρ = 1 × 10³ kg/m³ for water).

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 that 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 neighbouring 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 moves.

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

1. It is responsible for the different rates of flow of fluids.
2. It affects the 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 the stone. At this point, the stone moves with constant velocity because its acceleration 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 of 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.