## Question

A non-viscous liquid of constant density 1000 kg/m^{3} flows in a streamline motion along a tube of variable cross-section. The tube is kept inclined in the vertical plane as shown in figure. The area of cross-section of the tube at two points *P* and *Q* at heights of 2 metre and 5 metre are respectively the velocity of the liquid at point *P* is 1 m/s. Find the work done per unit volume by the pressure and the gravity forces as the fluid flows from point *P* to *Q*.

### Solution

29025 J

As gravitational field is conservative, i.e., *W* = –*U*

So work done by the force of gravity per unit volume

Now in case of ideal fluid motion by conservation of mass, i.e.,

Now as work done per unit volume by pressure,

But by Bernoulli’s theorem,

which in the light of eq. (i) and (ii) yields

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