Introduction to motion in fluids

Introduction to motion in fluids. When a body falls through a fluid it will be acted on by three forces namely:
i) weight of the body
ii) viscous force (Viscous drag)
iii) up thrust

Directions of the above forces.
i) Weight of body: down ward direction towards earth.
ii) Up thrust: upward direction
iii) Viscous force; direction opposite to that of motion

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Direction of motion
The direction of motion is determined by direction of the viscous force, which is a force that opposes motion like in the above body the direction of motion is down ward because the viscous force is acting in upward direction.

Describing motion of a body falling in a fluid

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-As the body falls, it accelerates first with a net force (resultant force) given by the equation.
F=W – (v+u) Or F=W – v – u

-As the body continues to fall, it attains a maximum uniform velocity called terminal velocity when weight of body (W) = Viscous force (v) + up thrust (u)

W = v + u Or W – v= u

Terminal velocity is the uniform velocity attained by a body falling through a fluid when the net force on the body is zero such that: Weight = Viscous force + up thrust

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BERNOULLI’S PRINCIPLE

It states that when the speed of the fluid increases, the pressure in the fluid decreases and vice versa.

Liquids flowing in a pipe have three kinds of energies, namely;

kinetic energy

potential energy

pressure energy

the sum of these three energies is a constant.

a) Liquid

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When the liquid flows through the uniform tube, the level goes on decreasing as shown in the diagram, the faster the liquid, the lower the pressure.

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The pressure falls in the in the narrow part B but rises again in the wider part C. This is because, since B is narrow, the speed at which the liquid moves through it is higher, hence the fall in pressure.

Note:

Fluid pressure changes with the rate of flow in the pipe

Speed of water is greater at the constriction

The order of pressure in the tubes decreases in the order A, C and B.

b) Gases

Bernoulli Effect in an air stream can be shown by blowing air between two sheets.

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When air is blown the two sheets come together because the air between them moves faster resulting in decrease of pressure between them.

Application of Bernoulli’s principle
i) When the fluid comes out of a jet, the speed increases as the pressure decreases.
ii) At the jet the gas comes out at high speed so the pressure is low at the jet. This results in air to be drawn in.
iii) A spinning ball takes a curved path because the ball drag air around causing air to pass more rapidly over one side than the other. This results in pressure difference that causes a resultant force on the ball.

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iv) An aero plane wing called aero foil is shaped so that air has to travel farther and so faster on the top than underneath. This results in a pressure difference that causes a resultant up ward force on the wing, thus it lifts.

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v) When two large vehicles pass each other, a force of attraction is experienced. This is because:
The speeding vehicles drag layers of air along with them. As these layers of air pass each other at high speed, they cause a pressure decrease.
This results in the vehicles being pushed towards each other.

Fluid flow
A fluid is a liquid or gaseous substance. There are two types of fluid flow namely:
i) Stream line flow
ii) Turbulent flow

Stream line flow or Steady flow or Laminar flow

Is the type of fluid flow where all the fluid particles that pass a given point follow the same path at the same speed.
Stream line flow occurs where the slope falls gently so that the fluid flows slowly and uniformly.
It is obtained by making the;

Diameter of the pipe wide
Fluid flow slowly and uniformly.

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Turbulent flow
Is type of fluid flow in which the speed and direction of the fluid particles passing any given point vary with time.

Turbulent flow occurs where the slope is so steep, such as at a water fall and when there is a constriction.
Due to constriction or steep slope, water tends to flow very fast and so disorderly.
It is obtained by making the;
Diameter of the pipe narrow
Fluid flow very fast and disorderly, by lying the pipe steeply.

Differences between streamline and turbulent flow.

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