QUESTION 1 In fluid mechanics, the material derivative is used to describe the rate of change of a physical quantity (such as velocity, temperature, or concen- tration) as experienced by a particle moving through a flow field. Given the velocity field of a fluid in two dimensions as
vec(V)(x,y,t)=u(x,y,t)hat(i)+v(x,y,t)hat(j)
where
u(x,y,t)
and
v(x,y,t)
are the velocity components in the
x
- and
y
-directions, respectively. (a) Define the material derivative
(D\phi )/(Dt)
for a scalar quantity
\phi (x,y,t)
in terms of the velocity components
u
and
v
. [2 marks]

Question

QUESTION 1 In fluid mechanics, the material derivative is used to describe the rate of change of a physical quantity (such as velocity, temperature, or concen- tration) as experienced by a particle moving through a flow field. Given the velocity field of a fluid in two dimensions as

vec(V)(x,y,t)=u(x,y,t)hat(i)+v(x,y,t)hat(j)

where

u(x,y,t)

and

v(x,y,t)

are the velocity components in the

x

- and

y

-directions, respectively. (a) Define the material derivative

(D\phi )/(Dt)

for a scalar quantity

\phi (x,y,t)

in terms of the velocity components

u

and

v

. [2 marks]

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