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

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

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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