Two U-tube manometers are connected to the same tube as shown in the figure. Determine difference of pressure between $X$ and $Y$. Take specific gravity of mercury as $13.6.$ $(g=10 \mathrm{m} {\mathrm{s}}^{-2}, {\mathrm{\rho }}_{\mathrm{Hg}}=13600 \mathrm{kg} {\mathrm{m}}^{-3} )$

A metallic square plate is suspended from a point $x$ as shown in the figure. The plate is made to dip in water such that the level of water is well above that of the plate. The point $‘x’$ is then slowly raised at constant velocity. Sketch the variation of tension $T$ in string with the displacement $‘s’$ of point $x$. 

Consider the Venturi tube of figure. Let area $A$ equal $5a.$ Suppose the pressure at A is $2.0 \mathrm{atm}.$ Compute the values of velocity $v$ at $‘A’$ and velocity $v\text{'}$ at $‘a’$ that would make the pressure $p$ at $\text{'}a\text{'}$ equal to zero. Compute the corresponding volume flow rate if the diameter at $A$ is $5.0 \mathrm{cm}.$ (The phenomenon at $a$ when $p$ falls to nearly zero is known as cavitation. The water vaporizes into small bubbles.) $(P_{\mathrm{atm}} = {10}^5 \mathrm{N} {\mathrm{m}}^{-2}, \rho = 1000 \mathrm{kg} {\mathrm{m}}^{-3}).$

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 $P_{\mathit{x}} –\mathit{ }{P}_{\mathit{y}}$