Question

The piston of a steam engine is S0 cm in diameter, and the maximum steam gage pressure is 1.4 MPa. If the design stress for the piston rod is 68 MPa, its cross-sectional area (m') should be most nearly:
(A) 40.4 × 10.4 (

B) 98.8 x 104

(C) 228.0x 10

(D) 323.0 x 10

Answer 1

Answer:

cross section area = 40.4 × $10^{-4}$ m²

Explanation:

given data

diameter = 50 cm = 500 mm

maximum steam gage pressure = 1.4 MPa

design stress = 68 MPa

to find out

cross-sectional area

solution

we get here piston area that is

piston area = $\frac{\pi}{4} d^2$   ...................1

piston area = $\frac{\pi}{4} 500^2$

piston area = 196349.54 mm²

and we know force is express as  

force  is = pressure × piston area    ............................2

force  is = 1.4 × 196349.54

force = 274889.356 N

and stress is express as

stress = $\frac{force}{cross\ section\ area}$    .................3

area = $\frac{274889.356}{68}$

area = 4042.4905 mm²

area = 40.4 × $10^{-4}$ m²

so correct option is (A) 40.4 × 10.4 (