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# When modeling fluid flows with small changes in ## Problem 46P Chapter 2

Fluid Mechanics | 2nd Edition

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Problem 46P

When modeling fluid flows with small changes in temperature and pressure, the Boussinesq approximation is often used in which the fluid density is assumed to vary linearly with changes in temperature. The Boussinesq approximation is ρ = ρ()[1 –β(T– To)], where β is assumed to be constant over the given temperature range; β is evaluated at reference temperature T0, taken as some average or mid-value temperature in the flow; and ρ0 is a reference density, also evaluated at T0. The Boussinesq approximation is used to model a flow of air at nearly constant pressure,P = 95.0 kPa, but the temperature varies between 20°C and 60°C. Using the mid-way point (40°C) as the reference temperature, calculate the density at the two temperature extremes using the Boussinesq approximation, and compare with the actual density at these two temperatures obtained from the ideal gas law. In particular, for both temperatures calculate the percentage error caused by the Boussinesq approximation.

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##### ISBN: 9780071284219

Fluid Mechanics was written by Sieva Kozinsky and is associated to the ISBN: 9780071284219. Since the solution to 46P from 2 chapter was answered, more than 236 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Fluid Mechanics, edition: 2nd. The answer to “When modeling fluid flows with small changes in temperature and pressure, the Boussinesq approximation is often used in which the fluid density is assumed to vary linearly with changes in temperature. The Boussinesq approximation is ? = ?()[1 –?(T– To)], where ? is assumed to be constant over the given temperature range; ? is evaluated at reference temperature T0, taken as some average or mid-value temperature in the flow; and ?0 is a reference density, also evaluated at T0. The Boussinesq approximation is used to model a flow of air at nearly constant pressure,P = 95.0 kPa, but the temperature varies between 20°C and 60°C. Using the mid-way point (40°C) as the reference temperature, calculate the density at the two temperature extremes using the Boussinesq approximation, and compare with the actual density at these two temperatures obtained from the ideal gas law. In particular, for both temperatures calculate the percentage error caused by the Boussinesq approximation.” is broken down into a number of easy to follow steps, and 156 words. The full step-by-step solution to problem: 46P from chapter: 2 was answered by Sieva Kozinsky, our top Engineering and Tech solution expert on 07/03/17, 04:51AM. This full solution covers the following key subjects: temperature, boussinesq, Approximation, Density, reference. This expansive textbook survival guide covers 15 chapters, and 1547 solutions.

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