Question

In giving a patient blood transfusion, a needle of length $3.14cm$ and internal diameter $0.4mm$ is used. If $4c.c.$ of blood passes through the needle in $1$ minute the height of the blood level in the bottle above the needle is approximately.[density of blood $=1.02gm/cc$; Viscosity of blood $=0.02poise$; $g=10m{s}^{-2}$]

• A. $85cm$
• B. $75cm$
• C. $65cm$
• D. $50cm$

Answer 1

Answer: (C)

$65cm$

From poisseullis equation,
$Q=\frac{\pi r^4\Delta P}{8\eta L}$----------(1)
$Q=4cc/60s=\frac{1}{15}c{m}^3/s$-------------(2)
So,
$\Rightarrow \frac{1}{15}=\frac{\pi (0.2\times {10}^{-4}\times 1.02\times 980\times h)}{8\times 0.02\times 3.14}$[from (1) and (2) $\Delta P=Pgh$]
$\Rightarrow h=65.326cm$
$\Rightarrow h\approx 65cms$