(i) Air (density=`rho`) flows through a horizontal venturi tube that discharges to the atmosphere. The area of cross section of the tube is `A_(1)` and at the constriction it is `A_(2)`. The constriction is connected to a water (density`=rho_(0)`) tank through a vertical pipe of lenght H. Find the volume flow rate (Q) of the air through tube that is needed to just draw the water into the tube.

(ii) A non viscous liquid of constant density `rho` flows in a stremline motion along a tube of variable cross section. The tube is kept inclined in the vertical plane as shown in the figure. The area of cross section of the tube at two points P and Q at heights of `h_(1)` and `h_(2)` are respectively `A_(1)` and `A_(2)`. The velocity of the liquid at point P is v. Find the work done on a small volume `DeltaV` of fluid by the neighbouring fluid as the small volume moves from P to Q.

Answer

(i) `Q=sqrt((2rho_(0)gH)/(rho)[(1)/(A_(2)^(2))-(1)/(A_(1)^(2))]^(-1))`
(ii) `(1)/(2)rhoDeltaV((A_(1)^(2))/(A_(2)^(2))-1)v_(1)^(2)+rhoDeltaVg(h_(2)-h_(1))`