The area of cross-section of a large tank is 0.5 m^{2}. It has a narrow opening near the bottom having area of cross-section 1 cm^{2}. A load of 25 kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is 40 cm above the bottom, will be ___________ cms^{$$-$$1}. [Take g = 10 ms^{$$-$$2}]

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5 $$\times$$ 10^{$$-$$4} is __________ kJ/m^{3}. Assume that material is elastic upto the linear strain of 5 $$\times$$ 10^{$$-$$4}.

An ideal fluid of density 800 kgm^{$$-$$3}, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from a to $${a \over 2}$$. The pressure difference between the wide and narrow sections of pipe is 4100 Pa. At wider section, the velocity of fluid is $${{\sqrt x } \over 6}$$ ms^{$$-$$1} for x = ___________. (Given g = 10 ms^{$$-$$2})

The velocity of upper layer of water in a river is 36 kmh^{$$-$$1}. Shearing stress between horizontal layers of water is 10^{$$-$$3} Nm^{$$-$$2}. Depth of the river is __________ m. (Co-efficient of viscosity of water is 10^{$$-$$2} Pa.s)