Question

P1.30 shows a gas contained in a vertical piston– cylinder assembly. A vertical shaft whose cross-sectional area is 0.8 cm2 is attached to the top of the piston. Determine the magnitude, F, of the force acting on the shaft, in N, required if the gas pressure is 3 bar. The masses of thepiston and attached shaft are 24.5kg and 0.5kg respectively. The piston diameter is 10cm. The local atmospheric pressure is 1 bar. The piston moves smoothly in the cylinder and g=9.81 m/s2

Answer 1

Answer:

1.737 kJ

Explanation:

Thinking process:

Step 1

Data:

Area of the shaft = 0.8 cm²

Combined mass of shaft and piston  = (24.5 + 0.5) kg

                                                             = 25 kg

Piston diameter                                   = 0.1 m

External atmospheric pressure          = 1 bar = 101.3 kPa

Pressure inside the gas cylinder      = 3 bar = 3 × 101.3 kPa

g                                                           = 9.81 m/s²

Step 2

Draw a free body diagram

Step 3: calculations

area of the piston = 0.0314 m²

Change in the elevation of the piston, $\deltaz$

$\delta$z = $\frac{PE}{mg}$

    = $\frac{0.2*10x^{3} }{25*9.81}$

    = 0.82 m

Next, we evaluate the work done by the shaft:

$W_{s} = F_{s} Z$

     = (1668) ( 0.082)

     = 1. 37 kJ

Net area for work done = A (piston) - Area of shaft

                                       = $\pi*(0.1)^{2} - 0.8 cm^{2}$

                                        = 77.7 cm²

                                        = 0.007774 m²

Work done in overcoming atmospheric pressure:

 Wₐ = PAZ

       =101.3 kPa * 0.007774 * 0.82

      =  0.637 kJ

total work = work done by shaft + work to overcome atmospheric pressure = 0.367 + 1.37

= 1.737 kJ Ans