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
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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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