# cylindrical tank

## Stresses on Thin-walled Pressure Tanks

The circumferential stress, also known as tangential stress, in a tank or pipe can be determined by applying the concept of fluid pressure against curved surfaces. The wall of a tank or pipe carrying fluid under pressure is subjected to tensile forces across its longitudinal and transverse sections.

## Amount of water inside the horizontal cylindrical tank

**Problem**

A closed cylindrical tank measures 12 ft. long and 5 ft. in diameter. It has to contain water to a depth of 3 ft when lying in the horizontal position. Find the depth of water when it is in vertical position.

## 01-02 Water flowing into cylindrical tank

**Problem 01**

Water is flowing into a vertical cylindrical tank at the rate of 24 ft^{3}/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 ft^{3}/min, the surface rises 6 in/min. Find the radius of the tank.

## 58 - 59 Maxima and minima: cylinder surmounted by hemisphere and cylinder surmounted by cone

## 53 - 55 Solved Problems in Maxima and Minima

**Problem 53**

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

## Solution to Problem 138 Pressure Vessel

**Problem 138**

The strength of longitudinal joint in Fig. 1-17 is 33 kips/ft, whereas for the girth is 16 kips/ft. Calculate the maximum diameter of the cylinder tank if the internal pressure is 150 psi.

## Solution to Problem 136 Pressure Vessel

**Problem 136**

A cylindrical pressure vessel is fabricated from steel plating that has a thickness of 20 mm. The diameter of the pressure vessel is 450 mm and its length is 2.0 m. Determine the maximum internal pressure that can be applied if the longitudinal stress is limited to 140 MPa, and the circumferential stress is limited to 60 MPa.

**Solution 136**

Based on circumferential stress (tangential):

## Solution to Problem 135 Pressure Vessel

## 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/m^{2}. (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/m^{2}? (c) If the internal pressure were increased until the vessel burst, sketch the type of fracture that would occur.