A single slider vertical engine shiwn in figure has a bore of 30.5 cm ...
Problem Statement
A single slider vertical engine has a bore of 30.5 cm and a 80 cm long connecting rod with a stroke of 40 cm. The mass of reciprocating part is 135 kg. When the piston is at quarter stroke and is moving downwards, the net pressure on it is 650 kN/m2. If the speed of the engine is 250 rpm, the turning moment on the crankshaft at the instant corresponding to the piston shown in the figure will be?
Solution
Given:
- Bore = 30.5 cm
- Connecting rod length = 80 cm
- Stroke = 40 cm
- Mass of reciprocating part = 135 kg
- Net pressure on piston = 650 kN/m2
- Engine speed = 250 rpm
Step 1: Calculate the piston area
The area of the piston can be calculated using the formula:
Area of piston = π/4 x (bore)2
Substituting the given values, we get:
Area of piston = π/4 x (0.305)2 = 0.0735 m2
Step 2: Calculate the force acting on the piston
The force acting on the piston can be calculated using the formula:
Force on piston = Net pressure x Area of piston
Substituting the given values, we get:
Force on piston = 650 x 103 x 0.0735 = 47.775 kN
Step 3: Calculate the velocity of the piston
The velocity of the piston can be calculated using the formula:
Velocity of piston = (2 x Stroke x Engine speed)/60
Substituting the given values, we get:
Velocity of piston = (2 x 0.4 x 250)/60 = 3.333 m/s
Step 4: Calculate the acceleration of the piston
The acceleration of the piston can be calculated using the formula:
Acceleration of piston = (2 x Stroke x Engine speed2)/60 x connecting rod length
Substituting the given values, we get:
Acceleration of piston = (2 x 0.4 x (250)2)/60 x 0.8 = 109.72 m/s2
Step 5: Calculate the inertia force of the reciprocating parts
The inertia force of the reciprocating parts can be calculated using the formula:
Inertia force = Mass of reciprocating parts x Acceleration of piston
Substituting the given values, we get:
Inertia force = 135 x 109.72 = 14827.2 N