Karteikarten
Flow similarity & dimensional analysis
Karten in diesem Stapel (28)
- 1If 2 flows of similar, what does this mean?When two flows are similar, it means that the properties of one can be simply obtained from the known properties of the other by applying known scaling factors.
- 2What is scale modelling?Scale modelling involves the construction of a small model of the building and measuring the surface pressures in a wind tunnel.
To be successful, it is necessary for the flow cover the model to be similar to the real flow. - 3What is meant by geometric similarity?They have the same shape.
- 4Any distance between two points on body A is related to the distance between the same points on body B by...Where KL is the length scale factor.
- 5What defines 2 flows as similar?Two steady flows are similar when the fluid elements which are initially at corresponding points in the two systems follow the same paths i.e. the mean streamlines are geometrically similar.
- 6If the flow over the model and the flow over the real building are similar, then it follows that...Where U1A is measured velocity at point 1 and UrefA is reference wind speed at point 1 (both in model)
- 7Therefore, velocity at point 1 in the real flw is...
- 8What is the velocity scale factor?The velocity scale factor is defined by the ratio of velocities at corresponding points on the two buildings and is a constant (the same everywhere in the flow).
If flow similarity is achieved, flow characteristics of real building from scale model can be determined.
- 9If velocities at corresponding points in 2 flows have same everywhere, wha t else occurs? And what is it determined by?Acceleration is also fixed everywhere.
Acceleration of small element at point is determined by mss of element and resultant force of the element. - 10What must be true for resultant accelerations in 2 flows to be in same directions?Resultant forces must be in same direction
Individual forces acting on element (pressure, shear stress, gravity) must be in fixed ratio. - 11What is mass of element determined by? What does this follow?Density of fluid and volume of element.
Densities at corresponding points must be in fixed ratio. Same for viscosities, as determined viscous shear forces. - 12General requirements for flow similarities summarised by (1/3):Conditions at boundaries of 2 flows must be similar i.e. same body shapes.
Similarity of conditions at boundaries e.g. pressure and velocity. - 13General requirements for flow similarities summarised by (2/3):Relevant physical properties (density, viscosity) are distributed similarly in the 2 flows. Usually concerned with uniform density and viscosity.
Therefore ratio of densities and viscosities at corresponding points in2 flows will be the same everywhere. - 14General requirements for flow similarities summarised by (3/3):Various scale factors (length, density, viscosity, velocity) are related in certain way, so forces on corresponding elements if fluid in fixed ratio at all point in 2 flows.
- 15What is dimensional analysis?i.e. flows are described by physical properties (acceleration, velocity, density, pressure). They all have dimension and unit of measurement.
e.g. velocity has dimension of length per unit time and unit of m/s. - 16What are fundermental dimensions?Mass, length, time.
- 17What is the principle of dimensional homogeneity?All terms in equations must have the same dimensions i.e. RHS cancels out LHS.
- 18What is a functional relationship?When a specific point, e.g. pressure distribution for a building, (for a given shape of the building) at a fixed point depends on e.g. U, p, mu, H.
P = f(U, p, mu, H)
g(P, U, p, mu, H) = 0 - 19What does the Buckingham Pi theory state?States that if there is a functional relationship between n physical parameters, q1, q2, ... qn of the form g(q1, q2, q3, ... qn) = 0
Then there is a functional relationship between n-m dimensionless parameters pi 1 , pi 2 ... pi n-m in form G(pi 1 , pi 2 ... pi n-m) = 0 - 20What are dimensionless parameters formed from? What is m usually equal to?The dimensionless parameters are formed from the physical parameters. The number m is (usually) equal to
the minimum number of fundamental dimensions required to specify the dimensions of all the parameters. - 21If a flow can be completely descirbed by relationship between nondimensional parameters, what can be seen?Shows immediately to the requirement for similarity. If two flows (around geometrically similar bodies) have the same values of the non-dimensional parameters, the flows will be similar.
- 22What do non-dimensional parameters show?he non-dimensional parameters show how the scale factors need to be combined for similarity.
- 23Show the above for Re?
- 24Applying Pi theorem step 1Write dependent variable (physical parameter of interest) and write independent variable (physical parameters which determine flow)
m usually = 3.
Number of dimensionless parameters given by n-m.
Then tabulate. - 25Applying Pi theorem step 2From independent variables, select m primary variables used to non-dimensinalise (n-m) variables, which include M, L, T
- 26Applying Pi theorem step 3Construct dimensionless group for n-m variables. D this by using dimensional homogeneity.
- 27Applying Pi theorem step 4Dimensionless groups in functional relationship G(Pi 1, Pi 2... Pi n-m) = 0
- 28For flows to be similar, what else do they need?They need to have the same values for Pi parameters.
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- Fluid Mechanics Karteikarten am Flow similarity & dimensional analysis, erstellt von Alice K am 09/02/2020.
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