answer these questions: 1. In your own words write down a clear and concise defi
ID: 2997731 • Letter: A
Question
answer these questions:
1. In your own words write down a clear and concise definition of each of the following fluid flow lines: timelines, pathlines, streaklines and streamlines. 2. State the flow conditions under which the latter three flow lines coincide with each other. 3. When a flow accelerates in the streamwise direction, what happens to the streamlines? (Hint: something to do with the distance between them). Why? 4. When a flow accelerates transversely (i.e. in the cross -stream direction) what happens to the streamlines? (Hint: something to do with their curvature). Why? 5. What is a stagnation point? 6. What is the cause of tip vortices on a finite length wing?Explanation / Answer
1. A stream line is the imaginary line in a fluid flow field at a particular instant of time in which the direction of instantaneous velocity of flow at any point is given by the tangent to the stream line.
A Path line is the locus of a particular fluid element in the flow field over a period of time. Since a fluid particle can move through one point multiple times at different instants of time path lines can form loop, can cross each other unlike a stream line.
A streak line is the line which connects all fluid elements which have gone through a particular point in flow field. This is what we get when we insert dye in a flow field (Neglecting diffusion of dye).
Time line is a set of fluid packets that form a line at some instant in time.
2. Under steady flow conditions all first 3 lines coincide.
3. When a flow accelerats in streamwise direction stream lines will come closer because for maitaining same mass flow rate as before now with a higher velocity it requires less area. Thus stream lines will come closer for reducing area.
4. When it accelerates in cross stream direction the curvature will decrease other wise the may cross each other which result in unphysical cases such as two velocity at a point etc.
5. A stagnation point in a flow field is where the flow velocity is zero.
6. The pressure of air just under the wing is higher than Patm and above the wing is less than Patm. Now each molecule has a tendency to go to lo Pressure area from high pressure area. It cannot go to top of wing by moving in forward or back ward direction. So the molecule underneath is pushed to sideways where there is Patm and are then pushed to top of the wing. This will give a rotating motion to the fluid elements. Now as the wing moves forward this fluid element which got circular motion keep on rotating because of inertia and the radius will become less and less because of viscosity. This we see as trailing vortex behind a wing.
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