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Fluid mechanics - Coggle Diagram
Fluid mechanics
Gerenal calculations
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Navier stokes equation, describes flow and speed of liquid and gases in generall
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Compressible flow
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Shocks Imagine you are a rigid heavy fat person in a fish market full of people like you (in the pre corona world). Now suddenly a bus is traveling at a great speed (you cannot run with that speed). Now, you will try to run as fast as you can but you have a limit to it. The bus will collide with you and everyone will have to forcefully (compressively) cling on the front of the bus. That phenomenon is called a shock disturbance or a shock wave. Consider people as air particles and bus as a blunt body.
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Normal shocks
- Supersonic flow upstream of a normal shock
- Subsonic flow downstream of normal shock
- Entropy increases over the shock and consequenuently total pressure
- Sonic throat area increases
- Very weak shock waves are nearly isentropic
Terms
p_0 and similar is the stagnation, the value if the flow i still, like in a big resourvar. Not alowed to use these formula on obluiqe shocks
p^* is the sonic parameter, where Ma=1
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Mach waves In the above example, the bus is a big blunt body. Imagine one of you is capable to run at that high speed. The disturbance created by that person will be weak but that will also give you a shock (the weakest shock). Now such a disturbance is called a Mach wave. Technically, in supersonic flows size of gas are capable enough to cause Mach wave generation. So, Mach waves are weakest isentropic waves in a supersonic flow field and the flow through them will experience only negligible changes of flow properties.
Over shocks is it adiabatiskt, därmed är stagnationstempen samma
Control volume
Conversation of mass 3.3
If the control volume has only a number of one-dimensional inlets and outlet
$$\int_{CV}\frac{\partial \rho}{\partial t} dV +\sum_i (\rho_i A_i V_i)_{out} - \sum_i (\rho_i A_i V_i)_{in}=0$$
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Bernoullis 3.5
Demands:
- Steady flow, many flow can be treated as steady at least when doing cv
- Incompressible flow, low velocity gas flow without significant changes in pressure, liquid flow
- frictionless flow
- Flow along a single streamline
(3.75)
$$p_1+\frac{\rho V_1^2}{1}+ \rho g z_1 =p_2+\frac{\rho V_1^2}{2}+ \rho g z_2 + h_{turbine}-h_{pump}+h_{friction}$$
Bernoullis for pipe flow
$$p_1+\frac{\rho V_1^2}{1} \rho g z_1=p_2+\frac{\rho V_1^2}{2}+\rho g z_2+\rho g h_{tot}$$
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Energy equation for steady flow (3.69)
$$\dot{Q}-\dot{W}_s-\dot{W}_v=-\dot{m}_1(\hat{h}_1+\frac{V_1^2}{2}+g z_1)+\dot{m}_2(\hat{h}_2+\frac{V_2^2}{2}+g z_2) $$
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Generall terms
Cavitation is a phenomenon in which rapid changes of pressure in a liquid lead to the formation of small vapor-filled cavities in places where the pressure is relatively low.
When subjected to higher pressure, these cavities, called "bubbles" or "voids", collapse and can generate a shock wave that is strong very close to the bubble, but rapidly weakens as it propagates away from the bubble.
Q&A
Why there is no boundary layer separation on a flat plate even though the friction is available there too?
There is no boundary layer separation on a flat plate because there is not an adverse pressure gradient reversing the flow of motion. A boundary layer is a thin region of a fluid, near a surface, that is flowing more slowly due to friction between it and the surface. Separation occurs when that thin layer is disturbed by a force acting in the opposite direction of flow. This force is called an adverse pressure gradient and is generally caused by the fluid moving more slowly downstream. On a flat plate, the fluid only slows down inside the boundary layer and is generally unaffected downstream.If you were to tilt the plate up, the fluid would flow faster over the top of the plate and then slow down as it moved farther along. This would create that adverse pressure gradient and eventually cause boundary layer separation. The same thing happens to a plane when it stalls. If you tilt the wings too far upwards, you get boundary layer separation and the wing stops generating lift.
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