Question

A sealed pressure cooker allows steam to escape only through an opening in the lid. a separate metal object, called a petcock, sits on top of the opening and prevents steam from leaving until the pressure within the cooker overcomes the weight of the petcock. the petcock and the periodic escape of steam prevents the dangerous buildup of pressure and keeps the pressure inside the cooker above atmospheric pressure. determine the mass of the petcock of a pressure cooker whose operational pressure is 100 kpa gage and has a round opening 4 mm in diameter. assume atmospheric pressure is 101 kpa.

Answer 1

The mass of the petcock of the pressure cooker is 0.257 kg.

The total pressure inside the cooker is= atmospheric pressure+Gauge pressure

=100 kPa+101 kPa=201*10^3 Pa

The area of the petcock is= (π/4)d^2=0.785*0.004^2=12.56*10^(-6) m^2

Now the mass of the petcock is calculated as

P=(F/A)=(mg/A)

201*10^3=(m*9.81/(12.56*10^(-6)

m=0.257 kg

Therefore the mass of the petcock is 0.257 kg