Question

A pressure cooker cooks a lot faster than an ordinary pan by maintaining a higher pressure and temperature inside. the lid of a pressure cooker is well sealed, and steam can escape only through an opening in the middle of the lid. a separate metal piece, the petcock, sits on top of this opening and prevents steam from escaping until the pressure force overcomes the weight of the petcock. the periodic escape of the steam in this manner prevents any potentially dangerous pressure buildup and keeps the pressure inside at a constant value. determine the mass of the petcock of a pressure cooker whose operation pressure is 100 kpa gauge and has an opening cross-sectional area of 4 mm2. assume an atmospheric pressure of 101 kpa.

Answer 1

The weight of the petcock acts downwards and the pressure inside the cooker will act upwards. So the weight of petcock (W) is balanced by gage pressure inside the cooker.

Here the mass of petcock is m

the gage pressure acting inside the cooker is

the cross sectional area of opening is A

the acceleration due to gravity is g

substitute ,, and

Thus the weight of the petcock is 0.040775 kg