Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Stroke and Bore of a Piston


Date: 05/11/2000 at 01:21:40
From: Frank Walsh
Subject: Stroke and bore of a piston

A double-acting diesel engine for a ship has eight cylinders with bore 
1 m and stroke 1.3 m. The piston-rod diameter is 150 mm.

Determine:

a) The capacity of the engine.

b) The distance between the top face of the piston and the top of the 
cylinder head in the Top Dead Center (TDC) position, and the distance 
between the bottom face of the piston and the bottom of the cylinder 
in the Bottom Dead Center (BDC) position for a compression ratio of 
18:1 on both sides of the piston. Assume the compression starts at the 
extreme stroke positions and that the piston and cylinder heads are 
flat.

Answers: a) 16.15 m^3
         b) 76.5 mm, 74.8 mm

These are the answers in the book but it doesn't show how to work them 
out. I'm really stuck!

Thanks a million.


Date: 05/11/2000 at 05:45:06
From: Doctor Mitteldorf
Subject: Re: Stroke and bore of a piston

a) The capacity is the displaced volume, pi*R^2 times the stroke. 
Multiply by 8 for 8 cylinders. But the "double-acting diesel" gets 
power from both sides of the piston, so you get to almost double this, 
but not quite because the piston-rod takes up some volume. The 
effective area on one side is really pi*R^2, but on the other side 
it's pi*(R^2-r^2), where r is the piston rod radius = .075 m.

b) The minimum distance to the top and the maximum distance to the top 
must be in the ratio 18 to 1, and their difference must be the stroke, 
which is 1.3 m. A little algebra gives you the min and max. This gives 
the 76.5 mm answer. For the other side of the cylinder, where the 
effective bore area is reduced by the area of the piston-rod, they've 
reduced this by the ratio (bore-rod)/(total bore area). I can't 
imagine why they've done this.

- Doctor Mitteldorf, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Physics/Chemistry

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/