Determine the increase in pressure in vessel, Mechanical Engineering

Assignment Help:

Determine the increase in pressure in vessel:

A thin spherical vessel of diameter 750 mm & wall thickness 8 mm is filled through water at atmospheric pressure. Determine the increase in pressure if an additional volume of 1000 cc of water is pumped into the vessel. Young's Modulus of the material of the vessel is 2 × 105 N/mm2 and Poisson's ratio is 0.3. Take bulk modulus of water like 2 × 103 N/mm2.

Solution

Diameter of the vessel, d = 750 mm.

 Thickness, t = 8 mm.

Net increase in volume, dV = 1000 cm3 = 1 × 106 mm3.

Let enhance in pressure be p N/mm2.

Permitting for the compressibility of water, the added volume of water pumped in is the net change in volume because of enhance in the capacity of the vessel and reduces in the volume of water.

Hoop stress, σ  = pd/4t = p × 750/4 × 8 = 23.4375 p

Hoop strain, ε h  = (σh / E )(1 - v) = (23.4375 p/2 × 105) (1 - 0.3) = 8.203 × 10- 5 p

Volumetric strain, εv = 3 × εh

= 3 × (8.203 × 10- 5 ) p = 2.4609 × 10- 4  p

Original volume, V = π d 3 / 6

=( π× 7503 )/6

= 2.2089 × 108  mm3

Increase in the capacity of the vessel,

δV1 = εv × V

= (2.4609 × 10- 4 ) p × 2.2089 × 108  = 54359.6 p

Original volume of water in the vessel = 2.2089 × 108  mm3

Increase in pressure = p.

∴ Decrease in volume of water, δV 2   = (p / K  )V

= p/ (2 × 103)  = 2.2089 × 108 = 110445 p

Net volume change (added volume of water pumped in)

= Increase in capacity of vessel + Decrease in volume of water

δV = δV1 + δV2

1 × 106  = 54359.6 p + 110445 p

∴          p = 6.06 N/mm2.


Related Discussions:- Determine the increase in pressure in vessel

Bending stress, What is bending stress? The bending moment at section t...

What is bending stress? The bending moment at section tends to bend or deflect beam and internal stresses resist its bending. The process of bending stops when the cross sectio

#title.gear train, explain the working of gear trainAsk question explain de...

explain the working of gear trainAsk question explain detail#Minimum 100 words accepted#

Viscoelasticity, howto calculate area in hysteresisn..

howto calculate area in hysteresisn..

Show the procedure of welding of vessels, Q. Show the procedure of Welding ...

Q. Show the procedure of Welding of vessels? Welding of vessels, including pressure retaining parts and attachments thereto, shall be performed utilizing Welding Procedures, We

Hooks law, State Hook's law: Sol.: It states that when material is l...

State Hook's law: Sol.: It states that when material is loaded within the elastic limit, the stress is proportional to strain produced by the stress. This means that the rat

Steady state conditions and the thermal equilibrium state, What is a differ...

What is a difference between the steady state conditions and the thermal equilibrium state? In steady state condition, temperatures are constant although heat transfer is taking

Objectives- computer algorithm for on-line scheduling , Objectives After...

Objectives After studying this section, you should be capable to understand: Cell aspects of scheduling, Conventional priority rules, Newer approaches to on line

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd