Write the limitations of Bernoulli’s equation..

 Consider a water jar of radius $R$ that has water filled up to height $H$ and is kept on a stand of height $h$ (see figure) . Through a hole of radius $r$  $(r << R)$ at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is $x.$ Then

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 $ )

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. . . . .

Fig. represents vertical sections of four wings moving horizontally in air. In which case the force is upwards

Two immiscible liquid are filled in conical flask as shown in figure. The area of cross section is shown, a small hole of area a is made in lower end of cone. Find speed of liquid flow from hole