Fundamentals of Fluid Mechanics Questions and Answers  


If there is enough information to take this into account, then yes you have to. If not you have to mention this in the assumptions.




No, you shouldn't make this assumption. Your answer should work for any type of duct as long as the intake is aligned with the $y$ axis.






At constant volume, there is a relationship between $dm_{\rm a}$ and $dm_{\rm l}$ (if a bit of air mass is added to the volume, you can find exactly what the bit of water mass must be removed). Use this relationship to get rid of $dm_{\rm l}$.




The crosssectional area of the reflected snow can (in fact, must!) be found through Bernoulli. It's indicated in the question statement that there is no friction, so Bernoulli's equation certainly applies. Also note that measuring crosssectional area of the reflected snow can't be done with certainty given the drawing dimensions (in the figure, it wasn't clear what $d$ of the reflected snow stood for exactly). Also, $B/\cos(30)$ is not the width of the reflected snow — build a 3D model of the snow with a sheet of paper to convince yourself of this. Albeit coming a bit later than I would like, thank you for the question: I can see how the dimension $d$ of the reflected snow was not clear in this respect and made a change in the figure in consequence.




Streamline is the line that is composed of the velocity vectors linked to one another. Particle path is the path of a fluid element in space and time. Note that at steadystate, the streamline and the particle path coincide. But when the flow is unsteady, they differ.




Start from the total energy transport equation. Find the answer without assuming an isentropic path. If you solve the problem assuming an isentropic path, would you get the same answer? Why or why not?




Yes you are missing a term! Don't make an assumption and remove terms unless you have no other option. Keep your expression as complete as possible.




I'll give you an extension until Tuesday 11:00. The quiz will take place on Tuesday, not tomorrow.




You have the right answer: there was a typo and it is now fixed.




I am not sure why you think the pressure term should vanish. You should explain your reasoning.




The work due to pressure in the ground frame scales with the product between pressure and velocity of surface where pressure is applied (i.e. velocity of the surface with respect to the ground). If you expand $H$ in terms of $P$ in your equation and rewrite, you'll find that this is exactly the case. I see nothing wrong with the equation you posted.




You can't apply the chain rule here. You can only apply the chain rule when converting a total derivative, not a partial derivative.



$\pi$ 