Why does velocity increase as pipe size increases in certain cases for circular pipe flow,constant flow/slope?

Question

Example: Flow=0.15 cfs, slope = 0.77%, n=0.010, pipe size = 5.66 inches diameter and 8-inch diameter.

Answer 1

You are confused because we are not talking about full flowing pipe, we are only talking about partially full pipe.

You need to use Manning's formula to calculate the velocity of each pipe, are you sure that you did it right? I can't really calculate it easily from the info that you supplied, but I can say this.

Velocity=(1.486/n) * R^(2/3) * Slope^(1/2)

Now since you say the the "n" and the slope of the two pipes are the same, it is clear that "R" for the 8 inch pipe must be greater than the "R" for the 5.66 inch pipe.

Now what is this "R"? It is the hydraulic radius, which is the area of flow divided by the wetted perimeter. There must be some weird examples where the larger pipe has a greater hydraulic radius FOR A GIVEN FLOW RATE. For example, with this amount of flow, the 5.66 inch pipe might be flowing at 3/4 full and the 8 inch pipe is flowing at half full, each with it's own hydraulic radius. Even though the 8 inch pipe has more area of flow, it also has more wetted perimeter, but it is the ratio of the two that is important.

UPDATE- you know, the more I think about it, It seems that the 5.66 inch pipe must be almost full, like 90%, and the 8 inch pipe is like 3/4 full, the smaller pipe would have a greater ratio of wetted perimeter to flow area than the 8" pipe.

Answer 2

The smaller pipe has more surface area compared to its volume. Drag is related to surface area which means it takes more energy to move an equivalent amount of water (based on cross-sectional area) in a smaller pipe than in a larger pipe.

What this means is for an equivalent amount of 'head' (elevation drop--potential energy), a larger pipe will carry more fluid / cross-sectional area than a smaller pipe.

......................................................

Edit: Ah, didn't read the question quite as thoroughly as Mugwump--good catch......Just skipped ahead to what I thought important which was absolute flow, not velocity with a fixed flow.

The principle remains the same that there will be less wetted surface area and less drag in the bigger pipe and therefore the flow will be faster.

With partially filled pipes the pipe closest to half full will generally have the fastest flow rate, but the calculation is trickier. At half full, the pipe has the least surface area to volume of water in the pipe thereby giving it the least drag

Answer 3

The flow is impeded only by friction beween moving fluid and stationary surface.

The surface is in a linear relationship with the diameter of the pipe, the mass of fluid varies with the square of the diameter(area of cross-section).

Therefore, as diameter increases, the ratio fluid:surface improves (becomes greater) - or putting it another way, a given particle of fluid has less chance of contacting the surface and being retarded.

Less retardation, more velocity. QED.

Answer 4

I`m no expert in fluid dynamics but could it be because there is less frictional resistance in a larger diameter pipe??

Answer 5

Used to use this formula every day in my job as a pump tester, alas that was 40 years ago and the old grey matter is getting fuzzy. Try Wiki flow velocity.
Hope this helps

Answer 6

Veocity in a circular pipe (under gravity) is given
by the Colebrook-White equation, a form of it is:-

V = -2sqrt(2gSD) log(k/3.7D+2.15v/Dsqrt(2gSD))

where :-

D - diameter
g - acceleration due to gravity
k - Nikuradse equivalent sand roughness size
S - Hydraulic gradient
v - kinematic viscosity(1.14x10^-6 m2/s at 15deg C)

Answer 7

conservation of mass is why.

The same water has to flow through a smaller opening at any interval of time where (somewhere else) a larger opening is letting the same water pass through.

Since the water amount is the same everywhere, the water has to speed up through the smaller opening to get enough through to make sure water doesn't back-up, compress, or otherwise change.

Answer 8

very confusing stuff. search into a search engine. that may help!

Answer 9

difficult point. look from yahoo and bing. it can help!