Air of density $1.2\,kg\,m^{-3}$ is blowing across the horizontal Wings of an aeroplane in such a way that its speeds above and below the wings are $150\,ms^{-1}$ and $100\,ms^{-1}$, respectively. The pressure difference between the upper and lower sides of the Wings, is ........ $Nm^{-2}$
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A thin vertical uniform wooden rod is pivoted at the top and immersed in water as shown. The container is slowly raised. At a certain moment, the equilibrium becomes unstable. If density of water is $9/5$ times the density of wood, then ratio of total length of rod to the submerged length of rod, at that moment is
Two capillaries of same length and radii in the ratio $1 : 2$ are connected in series. A liquid flows through them in streamlined condition. If the pressure across the two extreme ends of the combination is $ 1 m$ of water, the pressure difference across first capillary is...... $m$
A train with cross-sectional area $S _{ t }$ is moving with speed $v_t$ inside a long tunnel of cross-sectional area $S _0\left( S _0=4 S _{ t }\right)$. Assume that almost all the air (density $\rho$ ) in front of the train flows back between its sides and the walls of the tunnel. Also, the air flow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be $p _0$. If the pressure in the region between the sides of the train and the tunnel walls is $p$, then $p _0- p =\frac{7}{2 N } \rho v_{ t }^2$. The value of $N$ is. . . . .
A log of wood of mass $120 Kg$ floats in water. The weight that can be put on the raft to make it just sink, should be ....... $Kg$ (density of wood = $600 Kg/m^3$)
What is the velocity $v$ of a metallic ball of radius $r$ falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body ? (The densities of metal and of liquid are $\rho$ and $\sigma$ respectively, and the viscosity of the liquid is $\eta$).
Two identical cylindrical vessels with their bases at same level each contains a liquid of density $\rho$. The height of the liquid in one vessel is ${h_1}$ and that in the other vessel is ${h_2}$. The area of either base is $A$. The work done by gravity in equalizing the levels when the two vessels are connected, is
Glycerine of density $1.25 \times 10^3\,kg\,m ^{-3}$ is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends is $10\,cm ^2$ and $5\,cm ^2$ and pressure drop across its length is $3\,Nm ^{-2}$. The rate of flow of glycerine through the pipe is $x \times 10^{-5} m ^3 s ^{-1}$. The value of $x$ is $..............$.
If it takes $5\,minutes$ to fill a $15\,litre$ bucket from a water tap of diameter $\frac{2}{{\sqrt \pi }}cm$ then the Reynolds number for the flow is (density of water $= 10^3\,kg/m^3$ ) and viscosity of water $= 10^{-3}\,Pa.s$ ) close to