Q. 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.

Verified Solution

The rate of change of velocity V with respect to space S is:

$\frac{\pmb{\delta}V }{\pmb{\delta} S}=\frac{12 – 2.4}{3.2}= 3 m/s/m$

and the convective acceleration is:

$a_{s}=V\frac{\pmb{\delta}V }{\pmb{\delta} S}$

Hence at the beginning,

Convective acceleratio $a_{2.4}= 2.4 \times 3 = 7.2 m/s^{2}$

and at the end,

$a_{12}= 12 \times 3 = 36 m/s^{2}$