01-02 Water flowing into cylindrical tank

Problem 01
Water is flowing into a vertical cylindrical tank at the rate of 24 ft3/min. If the radius of the tank is 4 ft, how fast is the surface rising?
 

Problem 02
Water flows into a vertical cylindrical tank at 12 ft3/min, the surface rises 6 in/min. Find the radius of the tank.
 

Problem 02
Water flows into a vertical cylindrical tank at 12 ft3/min, the surface rises 6 in/min. Find the radius of the tank.
 

58 - 59 Maxima and minima: Cylinder surmounted by hemisphere and cone Jhun Vert Wed, 05/06/2020 - 03:56 pm

Problem 58
For the silo of Problem 57, find the most economical proportions, if the floor is twice as expensive as the walls, per unit area, and the roof is three times as expensive as the walls, per unit area.
 

Problem 59
An oil can consists of a cylinder surmounted by a cone. If the diameter of the cone is five-sixths of its height, find the most economical proportions.
 

53 - 55 Solved Problems in Maxima and Minima

Problem 53
Cut the largest possible rectangle from a circular quadrant, as shown in Fig. 40.
 

Problem 54
A cylindrical tin boiler, open at the top, has a copper bottom. If sheet copper is m times as expensive as tin, per unit area, find the most economical proportions.
 

Problem 55
Solve Problem 54 above if the boiler is to have a tin cover. Deduce the answer directly from the solution of Problem 54.
 

Solution to Problem 133 Pressure Vessel

Problem 133
A cylindrical steel pressure vessel 400 mm in diameter with a wall thickness of 20 mm, is subjected to an internal pressure of 4.5 MN/m2. (a) Calculate the tangential and longitudinal stresses in the steel. (b) To what value may the internal pressure be increased if the stress in the steel is limited to 120 MN/m2? (c) If the internal pressure were increased until the vessel burst, sketch the type of fracture that would occur.
 

Hydrostatic Pressure on Surfaces Jhun Vert Sat, 04/18/2020 - 08:52 pm

Total Hydrostatic Force on Plane Surfaces

For horizontal plane surface submerged in liquid, or plane surface inside a gas chamber, or any plane surface under the action of uniform hydrostatic pressure, the total hydrostatic force is given by
 

$F = pA$

 

where p is the uniform pressure and A is the area.
 

In general, the total hydrostatic pressure on any plane surface is equal to the product of the area of the surface and the unit pressure at its center of gravity.
 

$F = p_{cg}A$

 

where pcg is the pressure at the center of gravity. For homogeneous free liquid at rest, the equation can be expressed in terms of unit weight γ of the liquid.
 

$F = \gamma \bar{h} A$

 

where   $\bar{h}$   is the depth of liquid above the centroid of the submerged area.