Surface Area Calculations

[Liquidmetal]

What is the formula for calculating the outside surface area of a U shaped tube?

What is the formula for calculating the Inside surface area of a U shaped tube?

 

[masters]

What is the formula for calculating the outside surface area of a U shaped tube?

What is the formula for calculating the Inside surface area of a U shaped tube?

Hi Liquidmetal,

You would need to know the length of the U-shaped tube as well as its outside radius and inside radius.

The Surface Area would be the same as that of a cylinder: \(\displaystyle 2 \pi rh\)

If its a tube, the ends would be open, so there's no surface area there.

If the tubes were closed on each end, we'd have to add \(\displaystyle 2\pi r^2\)

Use the appropriate radii for the inside and outside.

 

[Liquidmetal]

I am trying to create a easy spreedsheet to calculate the outside and inside surface area of pipe U bends. If I had a 2" diameter Pipe, that was 6" tall with an outside width 10". Any suggestions how how to create a spreedsheet that can calculate this?

 

[Deleted member 4993]

I am trying to create a easy spreedsheet to calculate the outside and inside surface area of pipe U bends. If I had a 2" diameter Pipe, that was 6" tall with an outside width 10". Any suggestions how how to create a spreedsheet that can calculate this?

If you can post a picture with the dimensions - that will be very helpful. Also please tell us - why are you interested in the inside surface area. Your terminologies (e.g. "tall", "outside width"0 are confusing - at least to me. If I could understand the problem better - I could help you.

 

[soroban]

Hello, Liquidmetal!

I am trying to create a easy spreedsheet to calculate the outside and inside surface area of pipe U bends.
If I had a 2" diameter Pipe, that was 6" tall with an outside width 10".
Any suggestions how how to create a spreedsheet that can calculate this?

Since you don't mention the thickness of the pipe's walls, the two areas are equal.

I'm trying to visualize the pipe . . .

      : 2 :  -  6  -  : 2 :
    = *---*           *---* =
    : *:::*           *:::* 1 
    : *:::*           *:::* =
    :  :::.           .:::  :
    6  *:::*..     ..*:::*  :
    :   *::::::* *::::::*   5
    :     *:::::::::::*     :
    =         * * *         =
      :  - 5 -  :  - 5  - :

If we straighten out the pipe, we have a circular cylinder.

\(\displaystyle \text{The radius of the cylinder is: }\,R \,=\, 1\text{ inch}\)

\(\displaystyle \text{The length of the cylinder is: }L \,=\,5\pi + 2\text{ inches}\)

\(\displaystyle \text{The surface area is: }\;A \:=\:2\pi RL \;=\;2\pi(5\pi + 2)\text{ in}^2\)

 

[Deleted member 4993]

Hello, Liquidmetal!

I am trying to create a easy spreedsheet to calculate the outside and inside surface area of pipe U bends.
If I had a 2" diameter Pipe, that was 6" tall with an outside width 10".
Any suggestions how how to create a spreedsheet that can calculate this?

Since you don't mention the thickness of the pipe's walls, the two areas are equal.

I'm trying to visualize the pipe . . .

      : 2 :  -  6  -  : 2 :
    = *---*           *---* =
    : *:::*           *:::* 1 
    : *:::*           *:::* =
    :  :::.           .:::  :
    6  *:::*..     ..*:::*  :
    :   *::::::* *::::::*   5
    :     *:::::::::::*     :
    =         * * *         =
      :  - 5 -  :  - 5  - :

If we straighten out the pipe, we have a circular cylinder.

\(\displaystyle \text{The radius of the cylinder is: }\,R \,=\, 1\text{ inch}\)

\(\displaystyle \text{The length of the cylinder is: }L \,=\,5\pi + 2\text{ inches}\)

\(\displaystyle \text{The surface area is: }\;A \:=\:2\pi RL \;=\;2\pi(5\pi + 2)\text{ in}^2\)

Soroban,

This is why I wanted more accurate description. You assumed "If we straighten out the pipe, we have a circular cylinder". That can only be assumed when the straight section of the pipe is much larger than the bend radius (r << l). In the case you assumed - the stright length ~1" and the bend radius 5". The length of the "inner line" of the tube is ~11" (?*3+2) and the "outer line" of the tube is ~17". To be cylinder - those two lengths need to be approximately equal.

 

[soroban]

Hello, Subhotosh!

Of course, you are correct.

I took the "easy way" and assumed we have a straight cylinder
. . which was bent into a U-shape.

To be totally accurate, we need the surface area of half a torus
. . plus the two straight sections of pipe.

I thought I'd let someone else work that out . . .

My diagram was only my first guess at the situation.
And we're all waiting for a clearer explanation.
.