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#### kemoo

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a vessel ∆ pressure = 100 mmhg Q= 100 ml/min

what will the flow be if diameter increase by 50%?

A -100 ml/min

B- 500 ml/min

C- 300 ml/min

D- 700 ml /min

please need with explanation

#### prokhe

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hope this helps

poiseuille equation Q= ∆ pressure / R , where R is Resistance
and R is inversely proportional to (radius )^4 and r=D/2: where D is diameter

∆ pressure is constant and on rearranging the equation
so Q'=(D'/2)^4
and D'=D+D/2= 3D/2 ( increase by 50%)

on calculating, Q = 506.25 ml /min

• Mondoshawan

#### Mondoshawan

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B. 500 ml/min

Poiseuille's equation says that

which is the same as

where Q is the flow rate and r is the radius or d the diameter.
Rearranging for Q, you can see that Q = (blahblahblah) d^4.
so if your new d is (1.5)d, then your flow increases by a factor of around 5.
100 -> 500

I hope that helps - I totally explained it badly in another thread • Sabio
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