BR physics - continuity

[anbuitachi]

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In BR fluids and solids section they said, "you must know why larger flow areas produce greater flow velocities"

Is this a mistake? I thought smaller cross sec area = larger velocities? Thanks

 

[puravida85]

In BR fluids and solids section they said, "you must know why larger flow areas produce greater flow velocities"

Is this a mistake? I thought smaller cross sec area = larger velocities? Thanks

Well, they're right. It's pretty theoretical how that comes about but essentially it is because for a fluid flowing with a constant speed, this must occur:

Viscous ******ing force = Pressure differences at the two ends of the pipe

Setting that up gives us:

4πnLv = (p1-p2)A

When you solve for v you eventually get:

v= (p1-p2)r^2/ 4nL

Therefore doubling r will increase velocity by 4. There are other ways I can show you this but this is I believe, sufficient enough. You can always think of how Q (Flow Rate) is derived, and you'll also see some proof as to why. Let me know if this has helped clear your thoughts.

 

[joshto]

r^4

 

[anbuitachi]

Oh I was thinking of the continuity instead of flow rate. I get it now, thanks