Re: GAMSAT Physics Fluids and Solids

A fluid is either a liquid or a gas. The molecules in a fluid are not arranged in any order or structure and thus move about in random directions relative to each other. The molecules of a fluid bond weakly, spin, and move past each other.

The molecules in solids are held in place by permanent molecular bonds. The molecules bond strongly and vibrate in a fixed position.

Density
Density (ρ) can be defined as the amount of mass (m) a fluid contains in a specified volume (V). It is defined as the ratio of its mass to its volume.

ρ = m/V

ρ = density, m = mass, V = volume

The units for density are Kg/m3
Students should know that density increases as you from gas to liquid to solid.

Density: solid > liquid > gas

Gases are the least dense and can be compressed, unlike solids and liquids, which for the GAMSAT are treated as incompressible.

Specific Gravity
Specific gravity is the ratio of the density of a substance to the density of water.

S.G. = ρsubstancewater

S.G. = specific gravity, ρsubstance = density of a substance, ρwater = density of water

The following 4 points must be learnt for the GAMSAT:

1. The density of water is 1g/ml = 1g/cm3; 1g/cm3 is the same as 103kg/m3

2. A specific gravity of less than one = substance lighter than water

3. A specific gravity of exactly one = substance equally as heavy as water

4. A specific gravity of more than one = substance heavier than water

We can use specific gravity of a substance to gain an intuitive understanding of the relative weight of the substance to water.

For example mercury has a specific gravity of 13.63, so lifting a container full of mercury will be equivalent to lifting 13.63 containers of water.

Pressure
Pressure problems arise in almost every GAMSAT exam. Pressure (P) can be defined as the force (F) per unit area (A):

P = F/A

F = perpendicular force to area in Newtons (N)

P = pressure in Pascal (Pa). 1 Pa = 1N/m2

A = area in square meters (m2)

Pressure can also be calculated as potential energy per unit volume. The following equation can be used to calculate different pressures in liquids at different depths. Pressure is calculated by multiplying density of fluid (ρ) with the acceleration due to gravity (g) and the depth below the surface of the fluid (h)

P = ρgh

P = pressure, ρ = density of fluid, g = acceleration due to gravity, h = depth below surface

It is important to understand the following characteristics of force and pressure of liquid fluids when solving these problems in the GAMSAT.

– At a certain depth, the pressure if the fluid is the same in all directions
– The shape or surface area of the container does not affect fluid pressure
– Fluids exert forces that are always at 90 degrees (perpendicular) to the surface of the container
– The pressure of a fluid is directly proportional to the density of the fluid and to its depth.

Buoyancy and Archimedes Principle
When an object is submerged in water (object replaces water) an upward force acts on the submerged object. This is termed the buoyant force.

Archimedes principle states that the buoyant force (Fb) is an upward force that acts on a submerged object, and is equal to the weight of fluid that is displaced by the submerged object.

The equation for the buoyant force is:

Fb = ρfluidVg

Fb = buoyant force, ρfluid = density of fluid, V = volume of fluid displaced, g = acceleration due to gravity

In previous years of the GAMSAT there have been questions that involve using the specific gravity of a fluid to determine the height of an object below or above the surface of the water.

The specific gravity of the fluid is equivalent to the height of an object partially submerged in the fluid.
If the specific gravity of the fluid is 0.5, then 50% of the height of the object will be immersed in the water and 50% of the height will be above the water. If specific gravity is 0.6, then 60% of the height will be immersed and 40% of the height will be above the water.

Fluids in Motion
Molecules of a moving fluid can be described as having two types of motion. These are laminar flow and turbulent flow.

Laminar flow is the fluid motion in which all the particles in the fluid are moving in a straight line. The particles within a layer are moving at the same rate and all particles are moving in the same direction.

Turbulent flow is an irregular flow of particles. Unlike the linear motion of laminar flow, the particles of turbulent flow move in a state of chaos, with some particles opposing the direction of others and causing collisions.

The rate of Laminar flow through a pipe can be determined by the following:
To determine the volume (V) past a point we multiply cross-sectional area (A) by length/distance (d).
Volume = (cross sectional area) x (distance)

Distance = (velocity) x (time)
d = vt

Therefore,
Volume = Avt
V = Avt

We have found the volume, now we can determine the rate (R):

Rate (R) is given by dividing the volume past a point by time.
R = (volume past a point) / time
R = Avt/t
R = Av

The continuity equation, which is used for a fluid in an enclosed tube can be written from the above equation:
A1V1 = A2V2
The subscripts 1 and 2 represent different points in the line of flow of a fluid.

Fluid Viscosity and Determination of Flow
Fluid velocity is defined as the resistance of fluid layers to flow past each other. The higher the viscosity of a fluid, the slower the fluid will flow. So if a fluid has a high viscosity coefficient (honey), it will flow slower than a fluid with a low viscosity constant (water).

Reynolds number (R) can be used to determine if the flow of a fluid is laminar or turbulent. The following equation is used:

R = vdρ/η

R = Reynolds number, v = velocity of flow, d = diameter of tube, ρ = density of fluid,
η = viscosity coefficient

When Reynolds number is less than 2000, flow in a pipe is generally laminar, and when greater than 2000, flow is generally turbulent.

Surface Tension
Surface tension can be defined as the intensity of intermolecular forces per unit length.

The surface tension of a liquid results from an imbalance of the cohesive forces between molecules:

1. A molecule in the bulk liquid experiences cohesive forces with other molecules in all directions.
2. A molecule at the surface of a liquid experiences only net inward cohesive forces.These cohesive forces between water molecules can allow some insects that are usually denser than water, to float and stride on the water surface.

Solids
Solids are elastic to some extent. They can change their dimensions by compressing or stretching, whilst maintaining their bonds.

Stress and strain are important concepts to understand when examining the elasticity of solids.

1. Stress is defined as the ratio of force applied to an object to the area over which the force is applied. The units for stress are N/m2
Stress = force/area

2. Strain is defined as the fractional change in dimension of an object caused by the stress. Strain has no units.

Stress and strain are proportional to each other, and this proportionality can be given as a ratio known as the modulus of elasticity (ME). To determine to modulus of elasticity, we simply divide the stress by the strain.
ME = stress/strain