## Question

Vessel whose bottom has round holes with diameter of 1 mm is filled with water. Assuming that surface tension acts only at holes, find the maximum height to which the water can filled in the vessel without leakage. Given that surface tension of water is

### Solution

3 cm

As shown in figure, here the vertical force due to surface tension at the hole will balance the weight *mg*, i.e.,

This *h* will be max when

= 0.03 m = 3 cm

#### SIMILAR QUESTIONS

The velocity of water in a river is 18 km/hr at the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The viscosity of water is 10^{–3} poiseuille.

The velocity of a small ball of mass *m* and density *d*_{1} when droped in a container filled with glycerine becomes constant after some time. What is the viscous force acting on the ball if density of glycerine is *d*_{2}?

Find the velocity of glycerine (having density 1.3 g/cc) if a steel ball of 2 mm radius (density = 8 g/cc) acquires a terminal velocity of 4 cm/s in falling freely in the tank of glycerine.

An area bubble of radius 1mm is allowed to rise through a long cylindrical column of a viscous liquid of radius 5 cm and travels at a steady rate of 2.1 cm per sec. If the density of the liquid is 1.47 g per cc, find its velocity. Assume g = 980 cm/sec^{2} and neglect the density of air.

Two equal drops of water are falling through air with a steady velocity *v*. If the drops coalesced, what will be the new velocity.

A spherical ball of radius and 10^{4} kg/m^{3} falls freely under gravity through a distance *h* before entering a tank of water. If after entering the water the velocity of the ball does not change, find *h*. The viscosity of water is .

Water flows through a capillary tube of radius *r* and length *l* at a rate of 40 ml per second, when connected to a pressure difference of *h* cm of water. Another tube of the same length but radius *r*/2 is connected in series with this tube and the combination is connected to the same pressure head. Calculate the pressure difference across each tube and the rate of flow of water through the combination.

Spherical particles of pollen are shaken up in water and allowed to settle. The depth of the water is . What is the diameter of largest particles remaining in suspension on hour later?

A cylindrical vessel of area of cross-section *A *and filled with liquid to a height of *h*_{1} has a capillary tube of length 1 and radius *r* protruding horizontally at its bottom. If the viscosity of liquid is , density and g = 9.8 m/s^{2}, find the time in which the level of water in vessel falls to *h*_{2}.

A ring is cut from a platinum tube of 8.5 cm internal and 8.7 cm external diameter. It is supported horizontally from a pan of a balance so that it comes in contact with the water in a glass vessel. What is the surface tension of water is an extra 3.97 g weight is required to pull it away from water? (*g* = 980 cm/s^{2})