Question

Pressure cookers have been around for more than$300$years, 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 is$25.0cm$in diameter and the gauge pressure inside is$300atm$? Neglect the weight of the lid.

Short answer

The force exerted by the pressure cooker is obtained as: $1.5\times {10}^{6}N$.

Step-by-step solution

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.

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 is$25cm$.

The radius R will be$25/2cm$.

The radius R in meter is$0.125m$.

The pressure P inside the cooker is$300atm$.

But in the formula we need to convert pressure into Pascal

The pressure P in Pascal $300\times 1.01\times {10}^{5}Pa$.

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

$$\begin{gathered} F=P\times A \\ =300\times 1.01\times {10}^5\times \left(\pi R^2\right) \\ =300\times 1.01\times {10}^5\times \left(\frac{22}{7}{\left(0.125\right)}^2\right) \\ =1.49\times {10}^6\text{N} \end{gathered}$$

Therefore, force exerted by the pressure cooker is:$1.5\times {10}^{6}N$.

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