1
$\begingroup$

I've been stuck on this for an hour. (Probem is below)

The problem is with part b. I understand its the basic mass flow in - mass flow out with air. The equation being $$\rho_{air}A_4V_4 = \rho_{air}A_0V_0$$ where we are trying to solve for $V_4$ or the speed of air coming in through pipe 4.

We rearrange to $$V_1=\frac{\rho_{air}A_0V_0}{\rho_{air}A_4}$$

Everything should cancel to

$$V_1=\frac{A_0V_0}{A_4}$$

The issue, what on earth is $V_0$???!

In part b, $\frac{dh}{dt}=0.1910\;\frac{ft}{s}$ and is the value I ASSUMED would be used for $V_0$ in this case but no, it gives a value of $27.5 \: \frac{ft}{s}$ which is not correct.

The value supposedly used for $V_0$ is 0.1484

What is this value? Where does it come from?

The only thing I can think of is that it has something to do with 'average velocity' as stated in the part b question.

Yet I'm drawing a complete blank. And have been for more time than I care to admit. Especially considering the solution is right in front of me.

Help is VERY appreciated at this point. enter image description here

$\endgroup$
0
$\begingroup$

In my opinion, this is a typo and your calculation is correct. In (a), the velocity at the boundary water-air is denoted $dh/dt$. Therefore, when considering only the air volume, and considering the air as incompressible, $$ \rho_{air}\,A_0\,\frac{dh}{dt}=\rho_{air}\,A_4\,v $$ as you wrote (though I would use $v$ instead of $V$ for the velocity, since $V$ is often associated with volume).

Using $dh/dt\approx 0.1910\,\mathrm{ft/s}$ yields $v\approx 27.5\, \mathrm{ft/s}$. Using instead the 0.1484 (ft/s) for $dh/dt$ that given in the solution for (b), $v$ calculates to 21.4 ft/s.

PS: Please, unlike the author of the problem, use units in your calculations.

PPS: You might check if there is a newer version of the textbook available, or if there is an errata.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.