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Molten steel is kept in a ladle. Due in natural convection. mixing occurs inside the melt. A 1cm diameter sphere is held in the centre of the melt where the steel flows upward. so as to measure the force exerted by the melt on the sphere. The force. F exerted by the melt on the sphere is given by $$F = f\left( {\frac{\pi }{8}} \right).\left( {\frac{{{\mu ^2}}}{8}} \right){\left( {\operatorname{Re} } \right)^2}.$$
Data: Density of liquid steels
= 7100 kg. m-3
Viscosity of liquid steel
= 6.5 × 10-3 kg. m-1. s-1
Reynolds number (Re) of the melt
= 5 × 103
Friction factor (f) = 0.3
The velocity of melt (m.s-1) in the central portion of the ladle would be
“What is the different between height and radius of solid cylinder?” Which of the following option is sufficient alone to find the answer? A) A solid cylinder is made by melting a solid sphere. The radius of cylinder is 3 times the radius of a circle whose area is 154 sq.m. Height of cylinder is equal to the height of cone whose volume is 2772 cubic meters. B) Area of a rectangle whose longer side is ¾ times the radius of a solid cylinder, is 168 sq.m and, Volume of solid cylinder is 2772 cubic meters and its height is 18 m. C) A metallic cone of radius 15m and height 35m is melted into the solid cylinder of radius equal to the radius of a circle whose area is equal to the area of rectangle whose sides are in the ratio 4 : 3 respectively. D) The curved surface area of the solid cylinder is 3 time the surface area of a sphere of radius 7m and height of cylinder is equal to the height of a metallic cone whose curved surface area is 308 sq.m. 
In this question two quantities are given. Find and compare them and choose the appropriate options. A cylinder of radius R and height H has the same volume as that of a sphere of radius r. The surface area of sphere is more than the curved surface area of cylinder. Quantity I: x, where 9x – 2 = 0 Quantity II: R/H; where a cylinder of radius R and height H has the same volume as that of a sphere of radius r. The surface area of sphere is more than the curved surface area of cylinder.
If the dynamic viscosity of a fluid is 0.5 poise and specific gravity is 0.5, then the kinematic viscosity of that fluid in stokes is
A solid sphere of radius 13 cm is melted and its some part is used to cast a hollow sphere whose internal radius is 5 cm. What will be the thickness of the sphere if the surface area of solid sphere is equal to the total surface area of hollow sphere?
A steel ball (density ρsteel = 7200 kg/m3) is placed in an upward moving liquid AI (density ρal = 2360 kg/m3, viscosity μAl = 1 × 10-3 Pa.s and Reynolds number = 5 × 105). The force (F) exerted on the steel ball is expressed as F = fπR2(ρAl V2/2)
where, f is friction factor (= 0.2), v is the velocity of liquid AI and R is the radius of steel ball.
The force exerted on the steel ball is
The viscosity of a fluid in motion is 1 Poise. What will be it’s viscosity (in Poise) when the fluid is at rest?
Tina observed the following when she tested the specific gravity of milk to check for adulteration- the specific gravity was lesser than that of pure milk. She complained to the milk vendor and the next day checked the specific gravity again. This time it came in the range of the desired specific gravity. Can we be assured that this is pure unadulterated milk?
Given below are two quantities named A and B. Based on the given information, you have to determine relation between the two quantities. You should use the given data and knowledge of Mathematics to choose between the possible answers. Quantity A: Number of hemispheres that can be formed by melting a sphere having volume equal to the volume of right circular cylinder whose diameteris 6 cm and height is 4 cm. Also, radius of hemisphere formed is half the radius of sphere from which the hemisphere is formed. Quantity B: Number of ice cream cones that can be made from a right circular cylinder shape ice cream container having radius 6 cm and height 5 cm. Ice cream cone to be made should have height 4 cm and slant height 5 cm and there should be a hemisphere made on top of the cone having radius equal to the radius of cone.
Consider a given volume of liquid at a temperature T below Tm with a free energy G’. If some of the atoms of the liquid cluster together to form a small sphere of solid, the free energy of the system will change to G, given by________ (Assume V1 volume of the solid sphere, V2 volume of liquid, A is the solid/liquid interfacial area, γ solid/liquid interface free energy, G1 and G2 are the free energies per unit volume of solid and liquid respectively).