At steady-state, the bulk velocity remains constant in a pipe if the cross-sectional area is constant because of mass conservation. Therefore, the bulk velocity at the entrance of the pipe (the exit of the pump) is equal to the bulk velocity at the exit of the pipe. This doesn't depend on gravity or height difference. I'll give you 1 point bonus boost for your question.
 12.05.14
 Question by Student 201127101 Professor, I have a question about Moody diagram. If $\frac{e}{d}=0.001$ and ${Re}_{D}=5 \times {10}^8$, can I think $f=0.019$? In other words, can I think $f$ is constant when $\frac{e}{d} \geq 0.00001$ and ${Re}_{D} \geq {10}^8$?
 12.07.14
Yes, you can assume that $f$ is constant for a Reynolds number higher than $10^8$ for the range of $e/D$ shown on the right axis of the Moody diagram. I think this is kind of obvious from the figure.. So I'll give you just 1 point bonus boost for your question.
-- Bonus boost added to the scoresheet
 12.09.14
Question by Student 201127127
Professor, I have a question about 9th assignment #4. You said that "Five bends give a pressure loss of $0.8{\cdot}{\frac{1}{2}}{\rho}{u_b}^2$ each." And you drew bends of pipe on blackboard like that. But I think 'pressure loss due to bends' is depending on curving angle. So, I think that pressure loss due to bends of first section is bigger than section 2. What I think is wrong? (Is 'the pressure loss due to bends' independent with shape of bends?) I need your advice :)
This is a good observation. But, the drawing on the board was meant as a schematic to give a rough idea of how the system looks like. The schematic is not meant to say that there are 4 bends at 90 degrees and a fifth at 45 degrees. It is meant to say there are 5 bends. Exactly what the turning angle is for each bend is not known — all we know is the loss coefficient. I'll give you 1.5 points bonus boost for your question.
 Question by Student 201129104 Professor, I have a question about assignment#6 question 3. In this problem, use momentum conservation equation in cylindrical coordinates about $\theta$. After erase all of being zero, there are $\frac{\mu}{r}\frac {\partial}{\partial r}(r \frac{\partial v_\theta}{\partial r}) + \mu \frac{\partial^2 v_\theta}{\partial z^2} - \mu \frac {v_\theta}{r^2}$. How do I know each of it proportion to $\frac{1}{H^2}$ or $\frac{1}{R^2}$
 12.11.14
Hmm, you can not use a figure this way. Figures are reserved for drawings and schematics, and shouldn't be used for mathematics. Use to typeset the mathematics and get rid of the figure. Then I'll answer your question.
OK, I see you edited your post and I will answer your question. The terms proportional to $1/R^2$ are those where there is a second derivative with respect to $r$ or those proportional to $1/r^2$. Likewise, the terms with a second derivative with respect to $z$ scale with $1/H^2$. I think I explained this in class already, so I'll give you just 1 point bonus boost for your question.
 Question by Student 201327104 hello professor. in Assign9 Q5, what does it mean by 'The maximum pressure that the pipeline can sustain is 80atmospheres above atmosphereic pressure'. I understood this statement as Pmax = 81atm. But, there are also some students who think Pmax = 80atm. which one is true??
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