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I had a chemical engineering homework problem where I had to come up with a velocity profile for methanol flowing through a cylindrical tube, where viscosity and average velocity were given, but the only dimension given for the tube was diameter. Values were (D = 0.1 m, viscosity = 1.7x10^-3 Pa*s, and = 1.666x10^-2 m/s). The problem asked to find the magnitude of shear stress at the tube wall per unit of length, the magnitude of shear force per unit of length, and the pressure drop per unit of length.

For shear stress I calculated a magnitude of 2.26x10^-3 Pascals. Multiplying stress by Area (3.14*D^2/4), I got 1.774x10^-5 Newtons. But this shear force answer is not per units of length. Similarly, to solve for pressure drop and use Hagen Poiseuille equation, I would be missing the critical value length (L), since the only dimension in my homework problem they gave me is diameter.

Is there a mistake with how the question is asked? How can I find Pressure Drop and Shear Force per units of length when the only dimension I have is diameter?

Gregory
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Velocity profile does not require the length. And for the other items, they are asking "per unit length," which means you can set $L=1$. More precisely, if you get some answer for pressure loss in Pa, your unit would really be Pa/m, because each meter of tubing would result in that much pressure loss.

RC_23
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