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#1
01-27-2011
 USMLE Forums Guru Steps History: 1+CK+CS Posts: 378 Threads: 161 Thanked 118 Times in 65 Posts Reputation: 132
blood flow in vessel?

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

#2
01-27-2011
 USMLE Forums Scout Steps History: 1+CK+CS Posts: 12 Threads: 3 Thanked 2 Times in 2 Posts Reputation: 12
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
 The above post was thanked by: Mondoshawan (01-27-2011)
#3
01-27-2011
 USMLE Forums Master Steps History: 1+CK+CS Posts: 590 Threads: 31 Thanked 1,270 Times in 416 Posts Reputation: 1294
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
 The above post was thanked by: Sabio (01-27-2011)

 Tags Cardiovascular-, Physiology-

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