a$.$ The pressure inside a soap bubble of diameter $12$ inches is $196$ pascal more than the locat

$2$

atmospheric pressure. Find the surlace tension in the bubble.

b$.$ If the standard attrospheric is $760$ mm of meroury find its value in lerms of height of water

$2$

column in metre

A roller gate of cylindrical form of $4$ m diameter and length $8$ m retains water on one side in

$3$

such a way that when it is placed on the dam the water just spills out over the gate. What is the vertical component of force and its direction.

$4.$ A metallic body floats at the interface of mercury and water such that $40\%$ of its volume is submerged in mercury and remaining $60\%$ in water. Find its density

$2.$ a$.$ The velocity vector in a fluid flow is given as$,V=4x^{3}i-10x^{2}yj+2tk$ Find the acceleration vector of a fluid particle at $(2,1,3)$ at time $t=1$

$6.$ The velocity potential function is given by$,\frac{O}{?}=5(x^2-y^2),$ show that it represents a possible case of steady, incompressible and irrotational flow.

$3.$ A pitot$-$tube is used to determine the velocity of flow oil through a horizontal pipe. The difference of mercury level in the $U-$ tube differential manometer connected to the two tapings of the pitot$-$tube is $10$ cm $.$ Find the velocity of flow of oil. Take the coefficient of pitot$-$tube as $0\mathrm{.}98$ and sp$.$ gr$.$ of oil as $0\mathrm{.}8$

$26.$ The discharge of water through a pipe of uniform cross section, $0\mathrm{.}7068m^2$ is $0\mathrm{.}25$ cumec. If the pipe bends at $135$ with the initial direction of flow find the magnitude and direction of the force at the bend if the pressure of flowing water is $4{10}^{4}kg\frac{f}{m^2}$

$4.$ a$.$ Explain the experimental method of determination coefficient of velocity $C_v$ for a small orifice

b$)$ Show that for an external cylindrical mouthpiece, $Cd=0\mathrm{.}855$ if the ratio of area of jet at

venacontracta and area of the mouthpiece is $0\mathrm{.}62$

a$.$ The head over the crest of a triangular notch of central angle $$ is increased by $5\%$ Find the percentage increase in discharge through the notch. What is the corresponding increment in case of a rectangular notch.

b$.$ Derive the expression for maximum discharge over a Broad Crested weir

a$.$ Starting with the average velocity of flow derive the expression for head loss $h_i$ for the viscous flow through a pipe of length $L$ and diameter $D$

b$.$ An oil of viscosity $0\mathrm{.}1N-\frac{s}{m^2}$ and relative density $0\mathrm{.}9$ is flowing through a circular pipe of diameter $5$ cm and of length $300$ m at a rate of $3\mathrm{.}5$ litres $\frac{?}{sec}.$ Find the shear stress at the pipe