Question

The maximum gauge pressure in a hydraulic system is 5.0 atm. What is the largest mass that could be lifted by this system if the diameter of the piston is 75 cm?

Answer 1

The answer is 22815.5kg

Step-by-step explanation:

Before we even begin the numerical calculations we have to define what the gauge pressure is. Gauge pressure is the amount by which the pressure in any given fluid exceeds the atmospheric pressure of 1atm(101325Pa). The weight of the mass and the pressure exerted by the mass from the top of the piston is given by,

`W_(m) =mg\\P=W_(m) /A`

where g is the acceleration due to gravity. For the system to be able to lift this mass the pressure it exerts on the piston must be equal to the gauge pressure that the fluid in the system exerts on the piston from below. That is,

`P_(m)=W_(m)/A=mg/A=5atm`

`m*9.81/(\pi (0.75/2)^(2) )=5*101325Pa`

making m the subject of the equation we obtain for the m,

`m=22815.5kg`

This is the largest mass that can be lifted by this system.