# Question 4.6: The velocity components in 2-D flow are u = ax and v = by. S......

The velocity components in 2-D flow are u = ax and v = by. Show that a = -b if the components satisfy the continuity equation.

Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.

Given: u = ax and v = by

Hence,                                                 $\frac{\pmb{\delta}u}{\pmb{\delta} x}=a$                                                    (i)

and                                                      $\frac{\pmb{\delta}v}{\pmb{\delta} y}=a$                                                    (ii)

In order to satisfy continuity equation in 2-D, we have

$\frac{\pmb{\delta}u}{\pmb{\delta} x} + \frac{\pmb{\delta}v}{\pmb{\delta} y}=0$

Substituting the values from Eqs. (i) and (ii), we get

a + b= 0

Hence,                                                   a= -b

Question: 4.3

## A stream function in a 2-D flow is y = 2xy. Show that the flow is irrotational. Also determine the corresponding velocity potential Φ . ...

Writing the Laplace equation (4.18) of stream func...
Question: 4.4

## The velocity components are given as follows: u = (2x + y + z)t; ...

Continuity equation in 3-D is given by Eq. (4.6) a...
Question: 4.5

## A nozzle is so shaped that the velocity of flow along the centreline changes linearly from 2.4 m/s to 12 m/s in a distance of 3.2 m. Determine the magnitude of convective acceleration at the beginning and end. ...

The rate of change of velocity V with respect to s...
Question: 4.2

## For the velocity potential Φ = x²— y² , find the velocity components at point (4, 5). ...

Given:  Φ = x²— y² We know that \frac{\pmb{...
Given $D_{1}$ = 30 cm = 0.3 m, [latex...