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Pressure cookers have been around for more than300years, although their use has strongly declined in recent years (early models had a nasty habit of exploding). How much force must the latches holding the lid onto a pressure cooker be able to withstand if the circular lid is25.0cmin diameter and the gauge pressure inside is300atm? Neglect the weight of the lid.

Short Answer

Expert verified

The force exerted by the pressure cooker is obtained as: 1.5×106N.

Step by step solution

01

Conceptual Introduction

Fluid statics, often known as hydrostatics, is a branch of fluid mechanics that investigates the state of balance of a floating and submerged body, as well as the pressure in a fluid, or imposed by a fluid, on an immersed body.

02

Converting units of given data

The pressure is the rate of force appliedto the surface per unit area.

Here the open end is at height h so it will exert a force inside.

The diameter of the cooker is25cm.

The radius R will be25/2cm.

The radius R in meter is0.125m.

The pressure P inside the cooker is300atm.

But in the formula we need to convert pressure into Pascal

The pressure P in Pascal 300×1.01×105Pa.

03

Step 3: Force exerted by the pressure cooker

The force exerted by the pressure cooker will be themultiple of pressure exerted in the cooker to the area of the lid of the cooker

F=P×A=300×1.01×105×πR2=300×1.01×105×2270.1252=1.49×106N

Therefore, force exerted by the pressure cooker is:1.5×106N.

Also, the force is to be applied is immense amount of force.

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