Answer to Question #145693 in Mechanical Engineering for varma

Question

In the adjoining figure, the diameters vary linearly between the
entry and exit from d1 to d2 (d1 > d2) respectively. The
velocity at the entry is given by V⃗

1 = V1î m/s. Assume the

flow is incompressible and therefore, A1V⃗

1 = AV⃗ , where A & V⃗
are area and velocity of the nozzle at any section x = x (x ≤
L). Find [5]
a) V⃗
2 as a function of x
b) Acceleration of a fluid particle, a using Eulerian approach
c) Acceleration of the fluid particle, a using Lagrangian approach

Answer 1

Here in this question figure is missing and also values are not clear

Still we can have idea for solving this type of question as

change in velcoity over time can be written as

$dV=\frac{\delta V}{\delta S}dS+\frac{\delta V}{\delta t}dt$

$a_s=\frac{dV}{dt}$ , on putting value of dV we get acceleration as

$a_s=V\frac{dV}{d S}$