The Pitot tube shown in the figure is used to measure fluid flow velocity in a pipe of cross sectional area $S$. It was invented by a French engineer Henri Pitot in the early $18^{th}$ century. The volume of the gas flowing across the section of the pipe per unit time is (The difference in the liquid columns is $\Delta h, \rho_0$ and $\rho$ are the densities of liquid and the gas respectively) :-
$Q = \,2s\sqrt {\frac{{\Delta h{\rho _0}g}}{\rho }} $
$Q = \,s\sqrt {\frac{{2\Delta h{\rho _0}g}}{\rho }} $
$Q = \,s\sqrt {\frac{{\Delta h{\rho _0}g}}{\rho }} $
$Q = \,s\sqrt {\frac{{2\Delta h{\rho}g}}{{{\rho _0}}}} $
Is Bernoulli's equation unsteady? Explain .
Water flows through a frictionless duct with a cross-section varying as shown in figure. Pressure $p$ at points along the axis is represented by
A liquid flows through a horizontal tube. The velocities of the liquid in the two sections which have areas of cross-section $A_1$ and $A_2$ are $v_1$ and $v_2$ respectively. The difference in the levels of the liquid in the two vertical tubes is $h$ . The incorrect statement is
A wooden block of volume $1000\, cm^3$ is suspended from a spring balance. It weighs $12$ $N$ in air. It is suspended in water such that half of the block is below the surface of water. The reading of the spring balance is ...... $N$
Water flows steadily through a horizontal pipe of variable cross-section. If the pressure of water is $P$ at a point where flow speed is $v$ , the pressure at another point where the flow speed is $2v$ , is (Take density of water as $\rho $ )