Maximum pressure difference between inner and outer surface of a thin walled circular tube of radius r and thickness `Deltar(Deltar lt lt r)` so that tube won't break is (Breaking stress of the material is `sigma_(0))`

Maximum excess pressure inside a thin-walled steel tube of radius r and thickness /_\r (lt lt r) , so that the tube would not rupture would be (breaking stress of steel is sigma_("max")

A circular ring of radius R and mass m made of a uniform wire of cross sectional area A is rotated about a stationary vertical axis passing throgh its centre and perpendicular to the plane of the ring. If the breaking stress of the material of the ring is sigma_(b) , then determine the maximum angular speed omega_("max") at which the ring may be rotated without failure.

When a liquid moves steadily under some pressure through a horizontal tube, it moves in the form of cylindrical layers coaxial to the ends of the tube. The velocity of different layers is different. The velocity of the layer is maximum along the axis of the tube and it decreases as one moves towards the walls of the tube. According to Poiseuille, the rate of flow of liquid through a horizontal capillary tube varies as the relation V alpha (pr^(4))/(eta l) where l and r are the length and radius of the tube and p is the pressure different between the ends of the tube and is the constant of proportionality. When two capillary tubes through which the liquid is flowing are joined in series then the equivalent liquid resistance is

Two capillaries of small cross section are connected as shown in the figure. The right tube has cross sectional radius R and left one has a radius of r (lt R) . The tube of radius R is very long where as the tube of radius r is of short length. Water is slowly poured in the right tube. Contact angle for the tube wall and water is theta = 0^(@) . Let h be the height difference between water surface in the right and left tube. Surface tension of water is T and its density is rho . (a) Find the value of h if the water surface in the left tube is found to be flat. (b) Find the maximum value of h for which water will not flow out of the left tube .

A cylindrical tube of length l has inner radius a while outer radius b. What is the resistance of the tube between (a) its ends (b) inner and outer surfaces ? (The resistivitiy of its material is p)

A capilary tube is kept vertical and made to touch the surface of the liquid of surface tension T . If the radius of the capillary tube is 'r' . Then the force on the wall of the capillary tube is

Two satellites of the Earth move in a common plane along circular orbits, the radii being r and r-Deltar(Deltar lt lt r) . What is the time interval between their periodic approches to each other over the minimum distance Take to M_(c ) to be the mass of the Earth. (M_(c )=6xx10^(24)kg , r=7000km , Deltar=70km ).