Viscous Flow Questions & Answers | |
Please ask your questions related to Fluid Mechanics in this thread, I will answer them as soon as possible. To insert mathematics use LATEX. For instance, let's say we wish to insert math within a sentence such as $C_f$ is equal to $\tau_w /\frac{1}{2} \rho q_\infty^2 $. This can be done by typing \$C_f\$ is equal to \$\tau_w /\frac{1}{2} \rho q_\infty^2\$. Or, if you wish to display an equation by itself out of a sentence such as: $$ \frac{d}{dt}\int_V \rho dV + \int_S \rho (\vec{v} \cdot \vec{n}) dS =0 $$The latter can be accomplished by typing \$\$\frac{d}{dt}\int_V \rho dV + \int_S \rho (\vec{v} \cdot \vec{n}) dS =0\$\$. You can learn more about LATEX on tug.org. If the mathematics don't show up as they should in the text above, use the Chrome browser instead of Internet Explorer. Ask your question by scrolling down and clicking on the link “Ask Question” within the page footer. |
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Yes, you can assume $dP/dx$ to be the same when solving the rusted pipe and the smooth pipe. For this problem the pump can be assumed to yield constant pressure increase, and this pressure increase leads to a certain $dP/dx$ in the pipe which won't change as long as the pressure at the pipe exit and the pressure of the fluid entering the pump doesn't change. In this case, the pressure of the fluid entering the pump as well as the pressure at the exit of the pipe are atmospheric, hence why $dP/dx$ can be assumed not to vary. I'll give you 2 points bonus boost.
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You can proceed iteratively by trying out a correlation and checking if the correlation is valid once the answer is obtained. Or you can use the Moody diagram instead of using the correlations. I'll give you 1 point bonus boost.
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This is a good question. What you have to do is to make a table of $u_{\rm b}$ as a function of the number of nodes as follows:
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