Water is flowing in streamline motion through a horizontal tube. The pressure at a point in the tube is $p$ where the velocity of flow is $v$. At another point, where the pressure is $p/2$, the velocity of flow is (density of water $= \rho$)

Consider a cylindrical tank of radius $1\,m$ filled with water. The top surface of the water is at $15\,m$ from the bottom of the cylinder. There is a hole on the wall of the cylinder at a height of $5\,m$ from the bottom. $A$ force of $5 \times 10^{5}\,N$ is applied on the top surface of the water using a piston. Calculate the speed of efflux from the hole. (Given: atmospheric pressure $P_{A} = 1.01 \times 10^{5}\,Pa$,density of water $\rho_{w} = 1000\,kg/m^{3}$,and gravitational acceleration $g = 10\,m/s^{2}$) (in $,m/s$)

An $L$-shaped glass tube is just immersed in flowing water as shown. If the speed of the water current is $V$,then the height $h$ up to which the water rises will be

$A$ manometer connected to a closed tap reads $3.5 \times 10^5 \ N/m^2$. When the valve is opened,the reading of the manometer falls to $3.0 \times 10^5 \ N/m^2$. The velocity of the flow of water is ........ $m/s$.

An aeroplane of mass $3 \times 10^4\,kg$ and total wing area of $120\,m^2$ is in a level flight at some height. The difference in pressure between the upper and lower surfaces of its wings in kilopascals is........... $kPa$ $(g=10\,m/s^2)$

An $L$-shaped tube with a small orifice is held in a water stream as shown in the figure. The upper end of the tube is $10.6 \ cm$ above the surface of the water. What will be the height (in $cm$) of the jet of water coming from the orifice? The velocity of the water stream is $2.45 \ m/s$. (Take $g = 9.8 \ m/s^2$)