TAMU MEEN 344 - MEEN344_Practice_Problems_Exam2A (20 pages)

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MEEN344_Practice_Problems_Exam2A



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MEEN344_Practice_Problems_Exam2A

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Pages:
20
School:
Texas A&M University
Course:
Meen 344 - Fluid Mechanics
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Problem 7 1 2 Problem 7 2 2 Problem 7 3 Given Equation for beam Find Dimensionless groups 2 Solution Denoting nondimensional quantities by an asterisk A Hence A L2 A L2 A Substituting into the governing equation The final dimensionless equation is The dimensionless group is y y L t t y Ly t I t I L4 I L4 I x x L x Lx 2 y 4 y 4 1 L L A EL 4 LI 0 t 2 x 4 L 2 y E 4 y I 0 A t 2 L2 2 x 4 2 2 E 2 2 L Problem 7 5 4 Problem 7 6 2 Given Equations for modeling atmospheric motion Find Non dimensionalized equation Dimensionless groups Solution Recall that the total acceleration is r r r DV V r V V t Dt Nondimensionalizing the velocity vector pressure angular velocity spatial measure and time using a typical velocity magnitude V and angular velocity magnitude r r V V V Hence r r V VV r r p p p x r r p p p x L t t x Lx V L t L t V Substituting into the governing equation r r r r V V V r 1 p V V V V 2 V V p L t L L The final dimensionless equation is r r r V r p L r V V 2 p V t V 2 V The dimensionless groups are p V 2 L V The second term on the left of the governing equation is the Coriolis force due to a rotating coordinate system This is a very significant term in atmospheric studies leading to such phenomena as geostrophic flow Problem 7 7 Given Equations Describing pipe flow Find Non dimensionalized equation Dimensionless groups 2 Solution Nondimensionalizing the velocity pressure spatial measures and time u u V p p p x x L r r L t t V L Hence u V u p p p x Lx r Dr t L t V Substituting into the governing equation V u u 1 1 p 1 2 u 1 u V 2 p V L t L x t D r 2 r r The final dimensionless equation is p p L 2 u 1 u u t V 2 x DV D r 2 r r The dimensionless groups are p V 2 DV L D


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