Water flows through a horizontal tube of variable cross-section (figure). The area of cross-section at $x$ and $y$ are $40 {\mathrm{mm}}^2$ and $20 {\mathrm{mm}}^{2 }$respectively. If $10 \mathrm{cc}$ of water enters per second through $x,$ find

(i) the speed of the water at $x,$

(ii) the speed of the water at $y$ and

(iii) the pressure difference $P_{\mathit{x}} –\mathit{ }{P}_{\mathit{y}}$

Water flows through a horizontal tube of variable cross-section (figure). The area of cross-section at $x$ and $y$ are $40 {\mathrm{mm}}^2$ and $20 {\mathrm{mm}}^{2 }$respectively. If $10 \mathrm{cc}$ of water enters per second through $x,$ find

(i) the speed of the water at $x,$

(ii) the speed of the water at $y$ and

(iii) the pressure difference $P_{\mathit{x}} –\mathit{ }{P}_{\mathit{y}}$

Suppose the tube in the previous problem is kept vertical with $x$ upward but the other conditions remain the same. The separation between the cross-section at $x\mathit{ }$and $y$ is $\frac{15}{16} \mathrm{cm}$. Repeat parts $\left(\mathrm{i}\right), \left(\mathrm{ii}\right)$ and $\left(\mathrm{iii}\right)$ of the previous problem. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}.$

Water flows through a horizontal tube of variable cross-section (figure). The area of cross-section at $x$ and $y$ are $40 {\mathrm{mm}}^2$ and $20 {\mathrm{mm}}^{2 }$respectively. If $10 \mathrm{cc}$ of water enters per second through $x,$ find

(i) the speed of the water at $x,$

(ii) the speed of the water at $y$ and

(iii) the pressure difference $P_{\mathit{x}} –\mathit{ }{P}_{\mathit{y}}$

Figure here shows the vertical cross-section of a vessel filled with a liquid of density $\mathrm{\rho }$. The normal thrust per unit area on the walls of the vessel at a point $P$, as shown, will be

Two vessels $A$ and $B$ of different shapes have the same base area and are filled with water up to the same height $h$ (see figure). The force exerted by water on the base is $F_A$ for vessel $A$ and $F_{\mathit{B}}$ for vessel $B\mathit{.}$ The respective weights of the water-filled in vessels are $W_{\mathit{A}}$ and $W_B.$ Then,

(i) The cubical container$ABCDEFGH$ which is completely filled with an ideal (non-viscous and incompressible) fluid, moves in a gravity-free space with an acceleration of $a=a_0(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$ where a0 is a positive constant. Then the only point in the container shown in the figure where pressure is maximum is