Everything Thermofluids

What is a level curve in a MVF graph

A curve where a value stays constant

What assumption is made in order to partially differentiate

All the other variables are constants and the variables are independent

What is a partial derivative a measure of

How the function changes when just one variable is changed

What are mixed partial derivatives

2nd order with respect to 2 different variables

What do mixed partial derivatives show

The rate of change in one direction depending on another variable

Does the order you differentiation in for a mixed partial differentiation matter

No if they are continuous

What does a total differentiation tell us

How the function changes when the variables are varied simultaneously

What does differential form express

How something can change when both x and y change

What is an integrating factor

A function that is multiplied by to turn an inexact differential to an exact one

What is a fluid

A substance that flows rather than deforming

What is a shearing force

A force that acts in a direction parallel to the surface, causing one layer of the material to slide past another layer

What is shear stress

The internal force per unit area that resists the shearing force

What is the equation for shear stress

T = F/A

What can shear stress be quantified by

shear strain angle

What is shear strain angle

Shows how much a material shape deforms due to an applied shear stress

What happens to a shear strain angle in a fluid

It increases for as long as the stress is applied, irrespective of the magnitude of the shear stress

What happens to a shear strain angle in a solid

The angle increases up to a maximum value which depends on the magnitude of shear stress and then when it reaches the max it stays constant

What is the continuum hypothesis

The fluid is treated as a continuous substances with no gaps or holes

What does the continuum hypothesis mean for properties

They change smoothly from point to point

What is strain rate

The rate of change in shear strain angle

What is gamma in this equation

Shear strain angle

What is T is this equation

Shear strain

What is mu

Constant of proportionality

What is r in this

The radius of the circular path

What is Newtons Law of viscosity

The shear stress between fluid layers is directly proportional to the velocity gradient between the layers

What does shear stress induce on a fluid

A velocity gradient

What is Vx

The velocity of the fluid in the x direction

What is y

Vertical Position

What are Newtonian fluids

A fluid whose viscosity stays constant no matter how fast the fluid layers pass each other

What rule do Newtonian fluids obey

Newton’s Law of Viscosity

What is viscosity

The resistance to shear stress

What does the continuum approximation allow

Define fluid properties as if they are continuous variables

What is the dm referring to

Small amount of mass

What is dV referring to

Small value of volume

What is often used to compare densities and why

Specific gravity as it has no dimensions

How do you calculate specific gravity

Density of substance/ Density of reference

What s dF

Force normal to the area

What is dA

Small area

What is a compressive force

It acts to change the volume of the substances

Is a liquid a compressible fluid and what does this mean for its density

No, its density remains constant

Is a gas a compressible fluid and what does this mean for its density

Yes so its density is a variable

What are the three charateristics of pressure

The force resulting from pressure on a surface acts perpendicular, pressure at a point in a fluid a rest is the same in all directions, the pressure applied to the fluid is transmitted everywhere throughout the fluid

What is Pascel’s Principle

When a change of pressure is applied in an enclosed incompressible fluid, the pressure change is transmitted equally throughout the fluid in all directions

What does the pressure gradient due to gravity refer to

How the pressure changes as you move though the fluid due to the weight of the fluid above

What does p(z) stand for

Density at height z

How does pressure change with depth

It increases with depth

What must the fluid have to use the equation for pressure variation with depth

Constant density

What is Po

Pressure from where the depth is measured

What is gauge pressure

Pressure measured relative to atmospheric pressure

What is the equation for gauge pressure

Absolute pressure - atmospheric pressure

What is absolute pressure

Pressure measured relative to a vacuum

What is a planer surface

A perfectly flat surface

What does moment of a force refer to

The moment

What does P hat refer to

Average pressure

Where does the total force act

Centre of pressure

What is T

Total Moment

What is y_c

Centre of pressure

What assumption can we make about the center of pressure

It acts at the centroid

Where is the centroid for a square, circle and rectangular

The centre

Where is the centroid in a triangle

2/3 from the short side

When do you use these equations

For an unsubmerged gate at an angle

When do you use these equations

For a submerged water gate not at an angle

When do you use these equations

For a submerged gate at an angle

What is H bar

The average vertical depth of the centroid

What is Y bar

Centroid

What is the weight of v

Density times volume times gravity

What causes a buoyancy force

The pressure gradient

What is buoyancy force equal to

The weight of the fluid displaced by the body

In which direction does buoyancy force act

Upwards

What is another name for Archimedes’ Principle

Law of buoyancy

What does Archimedes’ Principle state

Any object that is wholly or partially submerged in a fluid experiences an upward buoyancy force equal to the weight of the fluid displaced

What are the 3 approaches to visualising fluid flow

Path line, Velocity fields and stream lines

What does a fluid path line follow

The path of a particle moving with the fluid

What does the particle tracing the path line have in common with the fluid surrounding it

Same direction and speed

What is the velocity in a velocity field a function of

Time and position

What do the arrows show on a velocity field graph

Magnitude and direction

What is a streamline

A curve though the fluid tangent to the local velocity at each point

How can the equation for a streamline be found

Solving the differential equation

What is a steady flow

A flow where the flow velocity at a point does not change with time

What is transient flow

A flow that changes for a short period before becoming steady

When are path lines and streamlines identical