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| skin friction=4fLV^2/2Dgc |
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friction loss due to contraction hfc=Kc=V^2/2 |
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| friction loss due to expansion=KeV^2/2 |
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| friction losses due to fittings |
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| f is a function of Re, f=0.046Re^-0.2, f=16/Re |
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| sections of pipe that have been divided from a single source |
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| connection point for pipes, pumps, etc |
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| what is the 3-step approach to solving complex piping? |
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1. continuity/ mass balance 2. MEB appplied to every pipe section that connects 2 nodes 3. equation for each pump |
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| Ma=u/a ratio of speed of fluid compared to speed of sound--speed of sound dependent on T, P of fluid |
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| For a converging, diverging nozzle how can we mix mass flow? |
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| Where does the limit to mass flow occur? |
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| What is the stagnation pt |
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| where velocity equals zero |
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| at max pipe length, what does MA equal? |
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| If we break through Ma, what happens? |
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| choked flow--> mass flow rate will change to prevent this |
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| What is the mass velocity? How can we get the mass flow rate? |
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Definition
| mass velocity, G=density *velocity, mass flow rate=G*A , Max G occurs when Ma=1 |
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| Difference between Kozeny-Carmen equation, Darcy's law, Burke Plummer equation and ergun |
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Definition
Darcy's law=pressure drop in bed, propotional to flow through bed Kozeny carmen is for Re<1 and first part of delta P/L=150... Burke-Plummer is for Re>1000 and is the second half of the ergun equation-ergun equation is for reynolds numbers between 1 and 1000 and is the entire thing |
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| for the ergun equation-small changes in porosity change * |
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| fully suspended particles |
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| What are the 2 main pump types? |
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Definition
| Centrifugal and positive displacement |
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| how does a centrifugal pump work? |
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Definition
| fluid enters the pump impeller at the center and is thrown outward through vanes on impeller at high velicty and enters discharge at high pressure |
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| how does a positive displacement pump work? |
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Definition
| fluid is drawn in through a check valve then is pushed out through another check valve as piston strokes |
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| For high pressure, what type of positive displacement pump should be used |
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Definition
| single-action plunger pump |
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| for a positive displacement pump if toxic or corrosive material what kind of pump |
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| rotary positive displacement |
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| close valve on discharge of pump don't do for positive displacement pump |
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| What are BHP, TDH, EFF and where are they found together? |
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Definition
BHP-brake horsepower TDH-total discharge head EFF-efficiency found together on pump curve |
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| how can you increase pressure on discharge of pump? Best choice |
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Definition
1. increase impeller size 2. increase impeller speed 3. increase input pressure best choice: increase impeller size |
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| What is the compression ratio? If this gets high what is a concern? How solved? |
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| Pb/Pa high >3 or 4, concern w hot temps! put compressors in series to avoid this |
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Definition
positive displacement "reciprocating" piston or diaphragm |
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| efficiency higher for pumps or compressors |
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| the force in the direction of flow exerted on the solid by the fluid |
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| drag due to pressure on object |
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| analogous to the friction factor for flow through a conduit |
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| if you have a sphere submerged within a flow stream, then, we consider the flow stream to look like this for extremely low Reynolds numbers |
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Definition
| this is called stokes' flow and requires that Rep<0.1 |
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| For low Re, stokes flow, if Re is increased? or when turbulent? |
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Definition
| if Re is increased u have a wake, and if turbulent your wake decreases |
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| How to minimize form drag? |
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Definition
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| what is terminal velocity |
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| where it can't go any faster |
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| phi s-surface area to volume ratio of particle |
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| void fraction or porosity- space not filled by particles |
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| equivalent channel diameter-size of channels that go through the bed in which the fluid flows |
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| avg velocity of fluid through bed |
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