Diameter to Volumetric Flow

[Zipper730]

Okay, I got a question: If diameter doubles and velocity of a fluid through a pipe remains constant, the volumetric flow increases by 4 right?

I figure that the area of a circle is: A = pi*(r)^2, and the formula for a cylinder is

1. V = (area of the base)*(h)
2. V = (pi(r)^2)*(h)

Correct?

 

[manta22]

Okay, I got a question: If diameter doubles and velocity of a fluid through a pipe remains constant, the volumetric flow increases by 4 right?

I figure that the area of a circle is: A = pi*(r)^2, and the formula for a cylinder is

1. V = (area of the base)*(h)
2. V = (pi(r)^2)*(h)

Correct?

Theoretically. In practice there is a boundry layer effect on the wall of the pipe so the flow is slightly greater than 4x.

 

[Zipper730]

manta22

What do you mean?

 

[pbehn]

Okay, I got a question: If diameter doubles and velocity of a fluid through a pipe remains constant, the volumetric flow increases by 4 right?

I figure that the area of a circle is: A = pi*(r)^2, and the formula for a cylinder is

1. V = (area of the base)*(h)
2. V = (pi(r)^2)*(h)

Correct?

Look at the equation. You have chosen "doubles" which means two times as big and the result is "four" which is two squared.

 

[manta22]

manta22

What do you mean?

In a small tube the boundry layer takes up a larger percentage of the tube's area, making it effectively "smaller" that it actually is, as far as flow is concerned. The larger tube has less effect from boundry layer so it will have slightly greater than 4X the flow of a tube half its diameter.

 

[pbehn]

In a small tube the boundry layer takes up a larger percentage of the tube's area, making it effectively "smaller" that it actually is, as far as flow is concerned. The larger tube has less effect from boundry layer so it will have slightly greater than 4X the flow of a tube half its diameter.

If it was as simple as the OP there wouldnt be a science of fluid dynamics. For example, the diameter isnt a constant, when the fluid pressure is increased the diameter of the pipe increases, but this is the fluid exerting a force on the pipe which leads to the boundary effects you mentioned. There is all sorts of "stuff" about viscosity, pressure velocity surface condition etc, just as there is with gases

 

[Zipper730]

In a small tube the boundry layer takes up a larger percentage of the tube's area, making it effectively "smaller" that it actually is, as far as flow is concerned. The larger tube has less effect from boundry layer so it will have slightly greater than 4X the flow of a tube half its diameter.

And if you correct for reynold's numbers you end up with the boundary layer not scaling up too much...