Blood of specific gravity 1 flows through an artery in the neck of a giraffe from its heart to the head. If the pressure at the beginning of the artery (outlet of the heart) is equal to 0.212 m of mercury, determine the pressure at the end of the artery when the head is:

(a) 2.4 m above the heart
(b) 1.8 m below the heart

Question

Blood of specific gravity 1 flows through an artery in the neck of a giraffe from its heart to the head. If the pressure at the beginning of the artery (outlet of the heart) is equal to 0.212 m of mercury, determine the pressure at the end of the artery when the head is:

(a) 2.4 m above the heart
(b) 1.8 m below the heart

Accepted Answer

Fig. 2.18 shows the position of heart 1 and neck 2 of the giraffe

(a) Applying Bemoullis equation between 1 and 2

[latex] \frac{P_{1}}{\gamma } + \frac{V^{2}_{1}}{2g} + z_{1}=\frac{P_{2}}{\gamma } + \frac{V^{2}_{2}}{2g} + z_{2}[/latex]

[latex] herefore \frac{P_{2}}{\gamma }=\left\lgroup\frac{P_{1}}{\gamma } ight group_{Hg} + z_{1} - z_{2}[/latex]

Equating pressure developed by column of mercury to column of blood, thus

.[latex] P= ho g h[/latex]

[latex] herefore \left( ho gh ight)_{Hg} = \left( ho gh ight)_{Blood}[/latex]

[latex] 13.6 imes 1000 imes 0.212 = 1 imes 1000 imes h_{Blood}[/latex]

[latex] h_{Blood} = 2.88 m[/latex]

[latex] herefore \frac{P_{2}}{\gamma } =\left\lgroup\frac{P_{1}}{\gamma } ight group_{Blood} + \left(z_{1} - z_{2} ight)[/latex]

[latex ] herefore \frac{P_{2}}{\gamma } = 2.88 + 0 - 2.4 = 0.48[/latex]

[latex] P_{2} = 0.48 imes 1000 imes 9.8 = 4.7 kPa[/latex]

(b) When the head is 1.8 m below the heart

[latex] \frac{P_{2}}{\gamma } = \left\lgroup\frac{P_{1}}{\gamma } ight group_{Blood} + z_{1} - z_{2}[/latex]

[latex] \frac{P_{2}}{\gamma } = 2.88 + 0 - \left( -1.8 ight)[/latex]

[latex] = 4.68[/latex]

[latex] P_{2} = 4.68 imes 1000 imes 9.8 Pa[/latex]

[latex] P_{2} = 45.8 kPa[/latex]

Question 2.5: Blood of specific gravity 1 flows through an artery in the n...

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