Piston Loading
Consider a steam engine's piston has a 10 in diameter, and a 1 in diameter piston rod. If the piston's rod has a design stress of 1,000 psi, what is the max steam gauge pressure in psi?
Expand Hint
$$$Pressure =\frac{Force}{Area}$$$
Hint 2
Since the piston force is the same force on the piston's rod, uniaxial loading is applied:
$$$\sigma =\frac{F}{A}$$$
where
$$\sigma$$
is the stress on the cross section,
$$F$$
is the loading, and
$$A$$
is the cross sectional area.
Uniaxial loading:
$$$\sigma =\frac{F}{A}$$$
where
$$\sigma$$
is the stress on the cross section,
$$F$$
is the loading, and
$$A$$
is the cross sectional area.
$$$F_{rod}=\sigma A_{rod}=(1,000\frac{lb}{in^2})(\frac{\pi}{4})(1in)^2=785\:lb$$$
To find the force on the piston caused by the steam pressure:
$$$\sum F=(pressure)(area)=(P)(\frac{\pi}{4} \cdot D^2)$$$
$$$F_{piston}=(P_{gauge})[\frac{\pi}{4} \cdot (10in)^2]$$$
Because
$$F_{piston}=F_{rod}$$
:
$$$785lb=(P_{gauge})[\frac{\pi}{4} \cdot 100in^2]$$$
Finding the max steam gauge pressure:
$$$P_{gauge}=\frac{785lb}{\frac{\pi}{4} \cdot 100in^2}=10\:psi$$$
10 psi
Time Analysis
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