Explanation Given information: dB sys dt = d dt ∫ cv ρb dV+ ∫ cs ρb V → r × n → dA Hint: Since B can be any property of the flow- scalar, vactor, or even tension − it can have a variety of dimensions. So, just let the dimension of B itself, {B}. Also, b is defined as B per unit mass. dB sys dt = d dt ∫ cv ρb dV+ ∫ cs ρb V → r × n → dA Here, In fluids there are ways to define fluid motion. There are two ways to define fluid motion: Lagrangian way of describing fluid motion Eulerian way of describing fluid motion In Lagrangian way, motion of fluid is defined by an individual fluid particle. It describes the motion of collection of fluid particles. In Eulerian way, motion is studied by defining a control volume through which fluid can flow in or out. The primary dimension of three additive in given equation can be written as: 1. { dB sys dt } = { B time } 2. { d dt ∫ cv ρb dV } = { 1 time × mass length 3 × B mass ×length 3 } 3. { ∫ cs ρb V → r × n → dA } = { mass length 3 × B mass × length time ×1×length 2 } Now, Dimension of heat transfer is: This is done to show law of homogeneity is valid or not. The dimension of the quantity on left must be equal to the dimension of the quantity on the right side in an equation of additive. In this question, the dimension of all the three additives must be similar. They are: 1. { dB sys dt } = { B time } { dB sys dt } = { B t } { dB sys dt } = { Bt -1 } 2

Fluid Mechanics: Fundamentals and Applications

4th Edition

ISBN: 9781259696534

Author: Yunus A. Cengel Dr., John M. Cimbala

Publisher: McGraw-Hill Education

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Chapter 7, Problem 19P

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The primary dimensions of each additive term in the given equation.

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Chapter 7, Problem 18P

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Fluid Mechanics: Fundamentals and Applications

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