AskSia

Plus

A 4 cylinder, 4 stroke marine oil engine has a cylinder diameter of 49 mm and a ...

Jan 1, 2024

The following data is available for 2-stroke diesel engine: Bore = 10 cm, stroke = 15 cm, engine speed = 1000 RPM, torque developed = 58 N-m, nm=80%, indicated thermal efficiency = 40%, calorific value of fuel = 44000 kJ/kg. Find: (a) Indicated power (b) Mean effective pressure and (c) Brake specific fuel consumption

Solution by Steps

step 1

To find the indicated power (IP), we use the formula:

IP = \frac{2 \pi N T}{60} \times \text{nm}

where

N

is the engine speed in RPM,

T

is the torque in N-m, and

\text{nm}

is the mechanical efficiency

step 2

Substituting the given values into the formula:

IP = \frac{2 \pi \times 1000 \times 58}{60} \times 0.80

step 3

Calculating the indicated power:

IP = \frac{2 \pi \times 1000 \times 58}{60} \times 0.80 = 61.6 \pi \text{ W}

Answer

Indicated power (IP) is approximately 193.65 W

Key Concept

Indicated power is the total power developed inside the engine cylinders

Explanation

Indicated power is calculated by considering the engine speed, torque, and mechanical efficiency. It represents the power developed by the combustion of fuel before any losses due to engine components.

step 1

To find the mean effective pressure (MEP), we use the formula:

MEP = \frac{2 \pi N T}{V_s}

where

V_s

is the swept volume per cycle in cubic meters

step 2

The swept volume

V_s

is calculated by:

V_s = \frac{\pi d^2}{4} \times S

where

d

is the bore diameter and

S

is the stroke length

step 3

Substituting the given values for bore (d = 0.1 m) and stroke (S = 0.15 m):

V_s = \frac{\pi \times (0.1)^2}{4} \times 0.15 = \frac{\pi \times 0.01}{4} \times 0.15

step 4

Calculating the swept volume:

V_s = \frac{\pi \times 0.01}{4} \times 0.15 = 0.00011775 \text{ m}^3

step 5

Now, we can calculate the mean effective pressure:

MEP = \frac{2 \pi \times 1000 \times 58}{0.00011775 \times 1000}

step 6

Simplifying the expression for MEP:

MEP = \frac{2 \pi \times 58}{0.00011775}

step 7

Calculating the mean effective pressure:

MEP = \frac{2 \pi \times 58}{0.00011775} \approx 978,000 \text{ Pa}

Answer

Mean effective pressure (MEP) is approximately 978 kPa

Key Concept

Mean effective pressure is a measure of the average pressure that acts on the pistons

Explanation

MEP is calculated using the torque, engine speed, and the swept volume of the engine. It is an indication of the engine's ability to do work and is independent of engine displacement.

step 1

To find the brake specific fuel consumption (BSFC), we use the formula:

BSFC = \frac{\text{Fuel Consumption Rate}}{\text{Brake Power}}

step 2

The brake power (BP) is given by:

BP = \frac{2 \pi N T}{60}

step 3

Substituting the given values into the formula for brake power:

BP = \frac{2 \pi \times 1000 \times 58}{60} = 61.6 \pi \text{ W}

step 4

The fuel consumption rate can be found from the indicated power and indicated thermal efficiency (

\eta_i

\text{Fuel Consumption Rate} = \frac{IP}{\eta_i \times \text{CV}}

where

\text{CV}

is the calorific value of the fuel

step 5

Substituting the indicated power and given values:

\text{Fuel Consumption Rate} = \frac{193.65}{0.40 \times 44000}

step 6

Calculating the fuel consumption rate:

\text{Fuel Consumption Rate} = \frac{193.65}{17600} \approx 0.011 \text{ kg/s}

step 7

Now, we can calculate the brake specific fuel consumption:

BSFC = \frac{0.011}{61.6 \pi \times 10^{-3}}

step 8

Simplifying the expression for BSFC:

BSFC = \frac{0.011}{61.6 \pi \times 10^{-3}} \approx 0.00056 \text{ kg/Ws}

step 9

Converting BSFC to more common units (g/kWh):

BSFC = 0.00056 \times 10^6 \text{ g/kWh}

step 10

Calculating the final value for BSFC:

BSFC = 0.00056 \times 10^6 \approx 560 \text{ g/kWh}

Answer

Brake specific fuel consumption (BSFC) is approximately 560 g/kWh

Key Concept

Brake specific fuel consumption is a measure of the fuel efficiency of an engine

Explanation

BSFC is the amount of fuel consumed per unit of power produced by the engine. It is an important metric for comparing the efficiency of different engines or engine settings.