# In a blood transfusion,blood flow from a battle at atmospheric pressure into a patient vein in which the pressure is 20mmHg higher than atmospheric.The bottle is 95cm higher than the vein and the needle into the vein has length of 3cm and diameter 0.45mm?

## how much blood flow into the vein each minutes? For blood $\eta = 0.004 p a . s$ and $\rho = 1005 \frac{k g}{m} ^ 3$ Ans: $3.4 c {m}^{3}$

Apr 21, 2018

Hagen-Poiseuille equation can be written as

ΔP = (128etaLQ) / (pid^4) ......(1)
where ΔP is the pressure difference between two ends of pipe, $\eta$ is the dynamic viscosity of fluid, $L$ is the length of pipe, $Q$ is the volumetric flow rate of fluid and $d$ is the internal diameter of the pipe.

Now $1 A t m = 760 \setminus m m H g = 101325 \setminus P a$. And

ΔP = "Pressure at the outlet of bottle" - "Pressure in the vein"
=>ΔP =(1\ Atm+ ρgh) -(1Atm+ 20/760 xx 101325)

Using given data and $\rho$ for blood and taking accleration due to gravity $g = 9.81 \setminus m {s}^{-} 2$ we get

=>ΔP = 1005 xx 9.81 xx 0.95 - 2666
=>ΔP = 6700\ Pa

Using (1) and inserting values in SI units we get

$6700 = \frac{128 \times 0.004 \times 0.03 \times Q}{\pi {\left(0.00045\right)}^{4}}$
$\implies Q = 5.619 \times {10}^{-} 8 \setminus {m}^{3} {s}^{-} 1$

Therefore blood flow volume per minute

$V = Q \times t = 5.619 \times {10}^{-} 8 \times 60$
$\implies V = 3.372 \times {10}^{-} 6 \setminus {m}^{3}$
$\implies V = 3.4 \setminus c {m}^{3}$, rounded to one decimal place.