As shown in the figure, a pump is designed as a horizontal cylinder with a piston having area $A$ and an outlet orifice having an area $a$. The piston moves with a constant velocity under the action of force $F$. If the density of the liquid is $\rho$, then the speed of the liquid emerging from the orifice is (assume $A \gg a$):

An ideal gas of density $\rho_1=0.2 \ kg \ m^{-3}$ enters a chimney of height $h$ at the rate of $\alpha=0.8 \ kg \ s^{-1}$ from its lower end,and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_1=0.1 \ m^2$ and the upper end is $A_2=0.4 \ m^2$. The pressure and the temperature of the gas at the lower end are $600 \ Pa$ and $300 \ K$,respectively,while its temperature at the upper end is $150 \ K$. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take $g=10 \ ms^{-2}$ and the ratio of specific heats of the gas $\gamma=2$. Ignore atmospheric pressure. Which of the following statement$(s)$ is(are) correct?

What is a venturi-meter? Explain its construction and working.

Water flows in a streamline motion through a horizontal pipe of circular cross-section. The pressure difference of water between $P$ and $Q$ is $15 \text{ Nm}^{-2}$. The area of cross-section at $P$ and $Q$ are $40 \text{ cm}^2$ and $20 \text{ cm}^2$, respectively. The rate of flow of water through the pipe, in $\text{cm}^3\text{s}^{-1}$, is : [Take density of water = $1000 \text{ kg m}^{-3}$]

Water from a tap emerges vertically downwards with an initial velocity of $4 \,m/s$. The cross-sectional area of the tap is $A$. The flow is steady and the pressure is constant throughout the stream of water. The distance $h$ vertically below the tap,where the cross-sectional area of the stream becomes $\frac{2}{3} A$,is (take $g = 10 \,m/s^2$): (in $\,m$)

$Assertion :$ The velocity of flow of a liquid is smaller when pressure is larger and vice-versa.
$Reason :$ According to Bernoulli's theorem,for the stream line flow of an ideal liquid,the total energy per unit mass remains constant.