Water flows into a large tank with a flat bottom at the rate of $10^{-4} \, m^3 s^{-1}$. Water is also leaking out of a hole of area $1 \, cm^2$ at its bottom. If the height of the water in the tank remains steady, then this height is ........ $cm$.

There are two holes,one each along the opposite sides of a wide rectangular tank. The cross-section of each hole is $0.01 \,m^2$ and the vertical distance between the holes is $1 \,m$. The tank is filled with water. The net force on the tank in newton when the water flows out of the holes is (Density of water $= 1000 \,kg/m^3$,$g = 10 \,m/s^2$)

$A$ cylinder contains water up to a height '$H$'. It has three orifices $O_1, O_2, O_3$ as shown in the figure. Let $V_1, V_2, V_3$ be the speed of efflux of water from the three orifices. Then

$A$ tank with vertical walls is mounted so that its base is at a height $H$ above the horizontal ground. The tank is filled with water to a depth $h$. $A$ hole is punched in the side wall of the tank at a depth $x$ below the water surface. To have maximum range of the emerging stream,the value of $x$ is

$A$ cylinder containing water stands on a table of height $H$. $A$ small hole is punched in the side of the cylinder at its base. The stream of water strikes the ground at a horizontal distance $R$ from the table. Then the depth of water in the cylinder is ............

$A$ cylinder containing water up to a height of $25 \ cm$ has a hole of cross-section $\frac{1}{4} \ cm^2$ in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out?