Problen $4(-F).|25$ Points$)$: Two blood vessels join to form a larger vessel as shown below. During a surgical procedure a needle accidentally pokes a hole with an ares of $0\mathrm{.}283c{m}^2,$ exposing the vessel to the surrounding open air. The pressures of the inlet vessels, $1$ and $2,$ are measured to be $750mmH($abs$)$ and $820mmHg($abs$)$ respectively, and the outlet vein pressure is $700mmHy.$ Use momentum conservation to determine the resultant force in the $y-$direction required to keen the vessel stationary, Assume blood has a density of $L\mathrm{.}06\frac{g}{c}{m}^3.$ Pressures are given in terms of absolute pressure.

$\frac{t}{b}ar(h{)}_1=20\mathrm{.}80\frac{g}{s}$

${}_1=100c\frac{m}{s}$

$P_1=750mmHg=1\mathrm{.}00{10}^6\frac{g}{cm*s}$

$A_1=0\mathrm{.}196c{m}^2$

mi $-$ mass flow rate

$v-$ velocity

P$-$ pressure

$A-$ area

$m_2=46\mathrm{.}85\frac{g}{s}$

${}_2=100c\frac{m}{s}$

$P_2=820mmH=1\mathrm{.}09{10}^4\frac{m}{cm-s}$

$A_2=0\mathrm{.}442c{m}^2$

A$.$ If the hole exposes the vesiel to the surrounding air, what is the pressure $[$g$($cmr$\text{'}$s$)($absolute$)]$ at the leak? Note: $[1Pa=10g[(cm-s))?$

$A=0\mathrm{.}283c{m}^2$

B$.$ Draw how the vector for the pressure force would act on the inlet and oiatlets of this system.

Page $10$ of $18$

AME:

UTD $1$D:

C$.$ Two assumptions we usually make for momentum conservation are plug flow and that the system can be treated as a particle. Determine$/$explain if these assumptions are appropriate for the system described above.

$)=(4CP$

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