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(a) A liquid of viscosity u flows in a circular pipe of radius r under a pressure gradient P. The flow rate, Q, in the pipe is calculated using the formula 84 If each of P, rand u have maximum errors of 1%, 3% and 2%, respectively, then use partial differentiation to determine the approximate maximum possible percentage error in the calculated flow rate, Q.

(a) A liquid of viscosity u flows in a circular pipe of radius r under a pressure gradient P. The flow rate, Q, in the pipe is calculated using the formula 84 If each of P, rand u have maximum errors of 1%, 3% and 2%, respectively, then use partial differentiation to determine the approximate maximum possible percentage error in the calculated flow rate, Q.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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05. (а) A liquid of viscosity µ flows in a circular pipe of radius r under a pressure gradient P. The flow rate, Q, in the pipe is calculated using the formula 84 If each of P, r and u have maximum errors of 1%, 3% and 2%, respectively, then use partial differentiation to determine the approximate maximum possible percentage error in the calculated flow rate, Q. (b) Consider the plane lamina S in the xy-plane which is bounded by the lines x=1, x =4, y = x² and y = 20. Sketch the region S and then calculate the centre of area (x,y) of this lamina.
Transcribed Image Text:05. (а) A liquid of viscosity µ flows in a circular pipe of radius r under a pressure gradient P. The flow rate, Q, in the pipe is calculated using the formula 84 If each of P, r and u have maximum errors of 1%, 3% and 2%, respectively, then use partial differentiation to determine the approximate maximum possible percentage error in the calculated flow rate, Q. (b) Consider the plane lamina S in the xy-plane which is bounded by the lines x=1, x =4, y = x² and y = 20. Sketch the region S and then calculate the centre of area (x,y) of this lamina.
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