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In fluid dynamics it is common to describe quantities that vary both with location (x, y, z) and with time (t), e.g. q=f(x, y, z, t). Dą _ aq *+ (v. ) q The total derivative of q is expressed as Dt at a) What are the names of the two terms on the right hand side, and what are their meanings? Dp b) If such quantity is the scalar density of the fluid, p in kg/m³, what principle does indicate? Dt

In fluid dynamics it is common to describe quantities that vary both with location (x, y, z) and with time (t), e.g. q=f(x, y, z, t). Dą _ aq *+ (v. ) q The total derivative of q is expressed as Dt at a) What are the names of the two terms on the right hand side, and what are their meanings? Dp b) If such quantity is the scalar density of the fluid, p in kg/m³, what principle does indicate? Dt

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
5th Edition
ISBN:9781305084766
Author:Saeed Moaveni
Publisher:Saeed Moaveni
Chapter18: Mathematics In Engineering
Section: Chapter Questions
Problem 17P
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In fluid dynamics it is common to describe quantities that vary both with location (x, y, z) and with time (t), e.g. 9-f (x, у, z, t). Dą _ aq (V.7) q The total derivative of q is expressed as + Dt a) What are the names of the two terms on the right hand side, and what are their meanings? DP. b) If such quantity is the scalar density of the fluid, p in kg/m³, what principle does indicate? Dt c) If the quantity is the vector velocity of the fluid, V = f(x, y, z, t) in m/s, what conservation principle is expressed as V.V = 0 ?
Transcribed Image Text:In fluid dynamics it is common to describe quantities that vary both with location (x, y, z) and with time (t), e.g. 9-f (x, у, z, t). Dą _ aq (V.7) q The total derivative of q is expressed as + Dt a) What are the names of the two terms on the right hand side, and what are their meanings? DP. b) If such quantity is the scalar density of the fluid, p in kg/m³, what principle does indicate? Dt c) If the quantity is the vector velocity of the fluid, V = f(x, y, z, t) in m/s, what conservation principle is expressed as V.V = 0 ?
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