Step-by-step explanation:
To calculate the indicated power, brake power, and mechanical efficiency of the steam engine, we need to use the given information and apply relevant formulas. Here's how we can calculate each value:
(a) Indicated Power:
The indicated power is a measure of the power developed within the engine cylinder. It can be calculated using the following formula:
Indicated Power (kW) = (2 * π * N * L * A * P) / (60,000)
Where:
N = Engine speed in RPM (200 RPM in this case)
L = Engine stroke in meters (convert 35 cm to meters)
A = Area of the indicator card (head-end card + crank-end card)
P = Average pressure on the indicator card
First, let's convert the engine stroke from centimeters to meters:
Engine stroke (L) = 35 cm = 0.35 m
Now, let's calculate the average pressure on the indicator card:
Average pressure (P) = (Head-end card pressure + Crank-end card pressure) / 2
Given:
Head-end card area (A1) = 25 cm²
Crank-end card area (A2) = 28 cm²
Length of cards (Lc) = 8.5 cm
Area of the indicator card (A) = A1 + A2 = 25 cm² + 28 cm² = 53 cm²
Now, let's calculate the average pressure (P):
Average pressure (P) = (Force on head-end card / A1) + (Force on crank-end card / A2)
Force on the head-end card = (Scale reading - Tare) * Spring scale
Force on the crank-end card = (Scale reading - Tare) * Spring scale
Given:
Spring scale = 25 kPa/mm
Scale reading = 370 kg
Tare = 150 kg
Force on the head-end card = (370 kg - 150 kg) * (25 kPa/mm)
Force on the crank-end card = (370 kg - 150 kg) * (25 kPa/mm)
Now, we can substitute the values into the formula to calculate the indicated power:
Indicated Power (kW) = (2 * π * N * L * A * P) / (60,000)
(b) Brake Power:
The brake power is the actual power delivered by the engine at the output shaft. It can be calculated using the following formula:
Brake Power (kW) = (2 * π * N * T) / 60,000
Where:
N = Engine speed in RPM (200 RPM in this case)
T = Torque measured at the output shaft
To calculate the torque (T), we can use the following formula:
Torque (T) = (Scale reading - Tare) * Spring scale * Brake arm length
Given:
Brake arm length = 1.5 m
Now, we can substitute the values into the formula to calculate the brake power.
(c) Mechanical Efficiency:
The mechanical efficiency of the steam engine can be calculated by dividing the brake power by the indicated power and multiplying by 100:
Mechanical Efficiency (%) = (Brake Power / Indicated Power) * 100
Now, you can perform the necessary calculations using the given values and formulas to determine the indicated power, brake power, and mechanical efficiency of the steam engine.