Interesting chemical engineering exam questions - 2 - With standard answers already available
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This post was last edited by yjqin1 on 2015-8-20 at 17:45. The background is as follows: it is a hollow fiber membrane whose inner diameter is much smaller than its length; the fluid flowing inside is an incompressible Newtonian fluid, and the flow is laminar. Assuming the volumetric flow rate of the fluid entering its pipe segment remains constant, what is the relationship between the pressure drop at the inlet and outlet and its inner diameter? A. Inverse proportion, B. Inverse proportion to its square, C. Inverse proportion to its cube, D. Inverse proportion to its fourth power
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The background is a hollow fiber membrane whose inner diameter is much smaller than its length, within which an incompressible Newtonian fluid flows in laminar flow. Assuming the volumetric flow rate of the fluid entering its pipe segment remains constant, what is the relationship between the pressure drop at the inlet and outlet and its inner diameter? B A. Inversely proportional, B. Inversely proportional to its square, C. Inversely proportional to its cube, D. Inversely proportional to its fourth power
I don’t know; wait for the expert to reply! ! ! ! ! ! ! ! !
B. inversely proportional to its square
The background is a hollow fiber membrane whose inner diameter is much smaller than its length, within which an incompressible Newtonian fluid flows in laminar flow. Assuming the volumetric flow rate of the fluid entering its pipe segment remains constant, what is the relationship between the pressure drop at the inlet and outlet and its inner diameter? B. It is inversely proportional to its square
A. It is inversely proportional. Why did so many people answer B? Did I misunderstand?
None of the answers are correct. The question I’ve set is flawless; to fully understand it, one needs to have systematically studied \"Principles of Transfer Processes\" – merely having studied \"Fundamentals of Chemical Engineering\" is not sufficient. But as long as you have studied principles of chemical engineering, you can give the answer. The Poiseuille equation △P=32μuL/d^2 is to be used; the answer will be given tomorrow.
This post was last edited by yjqin1 on 2015-8-20 17:16. Standard answer: D. It is inversely proportional to its fourth power. That is, with a constant volumetric flow rate, the pressure drop is inversely proportional to the fourth power of the inner diameter. In other words, those of us who work in membrane separation need to spin hollow fiber membranes (commonly referred to as membrane filaments). When manufacturing membrane filaments, the inner diameter must be controlled with great precision. For example, as a result of this deviation, if the inner diameter decreases by 10%, the volumetric flow rate will be reduced to 1/1.46 of its original value, which is equivalent to a 32% decrease. In other words: if the two membrane filaments are of the same length, a 10% difference in inner diameter results in a 46% difference in the volumetric flow rate through them.
Quality control engineers involved in the production of hollow fiber membranes must have a thorough understanding of this.