# Question 4.1: A pipe having diameter 30 cm at a section carries oil of spe......

A pipe having diameter 30 cm at a section carries oil of specific gravity 0.8 at a velocity of 2 m/s. At another section, the diameter is 20 cm. Find the velocity at this section and also the mass rate of flow of the oil.

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

Given $D_{1}$ = 30 cm = 0.3 m, $D_{2}$= 20 cm = 0.2 m, Specific gravity of oil s = 0.8 and $V_{1}$= 2 m/s
From continuity Eq. (4.3), we have

$Q=A_{1}V_{1}=A_{2}V_{2}$

Or                                                $\frac{\pi }{4}D^{2}_{1}\times2=\frac{\pi }{4}D^{2}_{2}\times V_{2}$

Or                                                 $V=(\frac{D_{1} }{D_{2} } )^{2}\times2=(\frac{0.3}{0.2} )^{2}\times 2=4.5 m/s$

Mass rate of flow of oil $=\rho _{\omicron }A_{1}V_{1}$

$=0.8\times 1000\times \frac{\pi }{4}\times(0.3)^{2}\times 2=113.097 kg/s$

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: 4.6

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

Given: u = ax and v = by Hence,                   ...
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. ...

Given:  Φ = x²— y² We know that \frac{\pmb{...