# Problem: Car Tires

How many car tires of the following approximate size can be filled with one tank of nitrogen with the following given specs?

• Tank Size: 200 scf (Standard Cubic Feet)
• Tire Pressure: 35 psi
• Starting Pressure: 2000 psi
• Rim Diameter: 18″
• Tire Diameter: 30 (Assume the inside of the tire is round like an O-ring.)

Example

a roll of paper has a 6″ OD and 1.5″ID.
6 – 1.5 = 4.5
4.5 x 0.70711 = 3.18″
3.18 + 1.5 = 4.68″ average diameter
Multiply this x Pi, and you will have the average circumference of 14.7″.
If you knew the thickness or number of raps, you could figure out the total length of that roll.

When trying to find an average diameter of a roll of paper, metal, or O-ring, etc., take the OD – ID and multiply that answer by 0.70711 (sin of 45°) and add the ID.

##### See the Solution

1.Find actual tank size. If we know the compression ratio, we can find CF (cubic feet) from SCF (standard cubic feet). Think of CF as compress volume and SCF as spongey volume of non-compress air. Formula is PSI / 14.7 + 1

A. Find C. R. (Compression ratio):  2000 PSI / 14.7 + 1 = 137: 1 C. R.

B. Volume of tank is 200 scf; 200 / 1.37 = 1.46 CF   Actual volume of tank (200 cubic feet of free air is compressed down to 1.46 cubic feet at 2000 psi.)

2. Find volume remaining in the tank at 35 psi that will not go into the tire:

A. Find C. R. for 35 psi; 35 / 14.7 + 1 = 3.38: 1   C. R. for the tire

B. Actual volume of tank 1.46 x 3.38 C. R. = 4.9 scf remaining in tank

C. Original volume of 200 – 4.9 of non-useable = 195.1 scf of useable volume

3. Find the cross section of the inside of the tire:

A. 30″ – 18″ = 12″ of tube / 2 sides = 6″ OD

B. Area of 6″:    6² x 0.7854 = 28.27 in²

4. Find length of tube, (if there was one)

A. Per given note:  30″ – 18″ = 12″

B. 12″ x 0.707 = 8.484″; 8.484 + 18 = 26.49″ average diameter

C. 26.49 x π = 83.2″ circumference

5. Find volume: A x L = V

A. 28.27 in² x 83.2 in = 2352 in³

B. 2352 / 1728 (cubic inches / cubic foot) = 1.36 cf per tire
1.36 cf x 3.38 C. R. = 4.6 scf / tire

6. Find number of tires:

A. 195.1 scf of tank / 4.6 scf / tire = 42.2 tires from one tank

### Deadline past. Not available for submissions.

By Ernie Parker, AI, AJPP, AJPPCC, S, MT, MM, MIH, MIP, MMH, Fluid Power Instructor, Hennepin Technical College, EParker@Hennepintech.edu

This teaser is printed in the Fluid Power Journal. Those who submit the correct answer before the deadline will have their names printed in the Society Page newsletter and in Fluid Power Journal. The winners will also be entered into a drawing for a special gift.