A piston of a steam engine is 300mm in diameter and the piston rod is of 50mmdiameter. The steam pressure is 1N/mm2. Find the stress in the piston rod andelongation of a length 800mm, taking E = 205KN/mm2, when the piston is on thestroke

To solve this problem, we need to follow these steps:

Step 1: Calculate the force exerted by the steam on the piston. The force (F) exerted by the steam on the piston can be calculated using the formula: F = P * A, where P is the pressure and A is the area. The area of the piston (A) can be calculated using the formula: A = π * (D/2)^2, where D is the diameter of the piston.

Given: P = 1 N/mm^2 D = 300 mm

A = π * (300/2)^2 = 70685.8 mm^2

F = 1 N/mm^2 * 70685.8 mm^2 = 70685.8 N

Step 2: Calculate the stress in the piston rod. The stress (σ) in the piston rod can be calculated using the formula: σ = F / A, where F is the force and A is the cross-sectional area of the rod. The cross-sectional area of the rod (A) can be calculated using the formula: A = π * (d/2)^2, where d is the diameter of the rod.

Given: F = 70685.8 N d = 50 mm

A = π * (50/2)^2 = 1963.5 mm^2

σ = 70685.8 N / 1963.5 mm^2 = 36 N/mm^2

Step 3: Calculate the elongation of the rod. The elongation (ΔL) of the rod can be calculated using the formula: ΔL = (F * L) / (A * E), where F is the force, L is the original length of the rod, A is the cross-sectional area of the rod, and E is the modulus of elasticity.

Given: F = 70685.8 N L = 800 mm A = 1963.5 mm^2 E = 205 KN/mm^2 = 205000 N/mm^2

ΔL = (70685.8 N * 800 mm) / (1963.5 mm^2 * 205000 N/mm^2) = 0.022 mm

So, the stress in the piston rod is 36 N/mm^2 and the elongation of the rod is 0.022 mm.

To solve this problem, we need to follow these steps:

Step 1: Calculate the force exerted by the steam on the piston. The force (F) exerted by the steam on the piston can be calculated using the formula F = PA, where P is the pressure and A is the area. The area of the piston (A) can be calculated using the formula A = π(D/2)^2, where D is the diameter of the piston.

Given: P = 1 N/mm^2 D = 300 mm

A = π*(D/2)^2 = π*(300/2)^2 = 70685.8 mm^2

F = P*A = 1 N/mm^2 * 70685.8 mm^2 = 70685.8 N

Step 2: Calculate the stress in the piston rod. The stress (σ) in the piston rod can be calculated using the formula σ = F/A, where F is the force and A is the cross-sectional area of the rod. The area of the rod (A) can be calculated using the formula A = π*(d/2)^2, where d is the diameter of the rod.

Given: F = 70685.8 N d = 50 mm

A = π*(d/2)^2 = π*(50/2)^2 = 1963.5 mm^2

σ = F/A = 70685.8 N / 1963.5 mm^2 = 36 N/mm^2

Step 3: Calculate the elongation of the rod. The elongation (ΔL) of the rod can be calculated using the formula ΔL = (FL)/(AE), where F is the force, L is the original length of the rod, A is the cross-sectional area of the rod, and E is the modulus of elasticity.

Given: F = 70685.8 N L = 800 mm A = 1963.5 mm^2 E = 205 KN/mm^2 = 205000 N/mm^2

ΔL = (FL)/(AE) = (70685.8 N * 800 mm) / (1963.5 mm^2 * 205000 N/mm^2) = 0.138 mm

So, the stress in the piston rod is 36 N/mm^2 and the elongation of the rod is 0.138 mm.