3. Assumptions, boundary conditions and problem solving

Question 1

What is a boundary?

Answer 1

A boarder of some 3D shape that provides a convenient border to a problem.

Question 2

What is a system?

closed system

Answer 2

a system is a boundary that can transfer heat and work but not mass.

Question 3

What is a open system?

also known as control volume (cv)

Answer 3

a system that can transfer heat, work and mass can cross

Question 4

State the Lagrangian approach.

Answer 4

A Langrangian approach means your box moves through space/through the flow domain (usually with a particle or small element of the flow)

• Effectively particle tracking through space so you need to break up the problem into small time steps.
• Easier with computers but not by hand.

Question 5

State the Eulerian approach.

Answer 5

A Eulerian approach means the box stays still and the flow moves through.

• Easier to do by hand than Lagrangian approach

Question 6

Define Steady flow.

Answer 6

The conditions (velocity, pressure and cross-section) may differ from point to point but DO NOT change with time.

• While in reality there may be high frequency changes in turbulance, over a long time frame it’s basically static.

If you look at the graph. Image a point anywhere on it. It stays in the same conditions over time at that specific point. But may be different to another point on the graph

Question 7

Define Unsteady flow.

Answer 7

If at any point in the fluid, the conditions change with time, the flow is described as unsteady.

• In practice there is always slight variations in the velocity and pressure, but if the average values are constant, the flow is considered steady.

Question 8

Define Uniform flow.

Answer 8

If the flow velocity is the same magnitude and direction at every point in the fluid it is said to be uniform.

Question 9

Define Non-uniform flow.

Answer 9

The flow velocity is not the same magnitude and direction at every point.

This graph shows steady flow, but also non-uniform flow too.

Question 10

Define the four different comibinations of flow below:

1. Steady uniform flow
2. Steady non-uniform flow
3. Unsteady uniform flow
4. Unsteady non-uniform flow

Answer 10

1. Steady uniform flow. Conditions do not change with position in the stream or with time.
2. Steady non-uniform where the flow rate is constant but the cross-sectional area of the pie changes. i.e. conditions change from point to point in the stream but do not change with time.
3. Unsteady uniform flow. At a given instant in time the conditions at every point are the same, but will change with time.
4. Unsteady non-uniform flow. Every condition of the flow may change from point to point and with time at every point. For example waves in a channel.

Question 11

Define Viscous flow.

Answer 11

• Viscous: Having a thick, sticky consistency between solid and liquid; having a high viscosity.
• A viscous liquid is thick and sticky and does not flow easily. It is resistant to a shearing stress.
• With viscous flow friction between fluid particles is strong. It cannot be ignored.

Question 12

Define an Invisicid flow.

Answer 12

Simply means that it has no viscosity. Particles are essentially frictionless with no heating effects, etc.

Inviscid flow is simpler to analyse. You do not have to account for the additional forces/mechanical energy losses.
There are some applications/regions of flow that can be approximated to be Inviscid.

• This essentially can help make unifrom flow in things like pipes.