CGPET 2021 Solved Paper

Given, heart pumps blood in volume per minutes, $AV=5\,\text{L/min}$ $AV = \frac{5 \times 10^{-3}}{60}\,\text{m}^3/\text{s}$ Here as shown in figure, area of arteries is $A$ and velocity of blood is $v$. Thus, the volume flows per second inside arteries is given by $(A \cdot v)$. Height of mercury, column, $h_{\mathrm{Hg}} = 150\,\mathrm{mm}$ $=150 \times 10^{-3}\,\text{m}$ Density of mercury, $\rho_{\mathrm{Hg}} = 13.6 \times 10^{3}\,\text{kg/m}^3$ and $g=10\,\text{m/s}^2$ Power (in watt) = ? In this case, we find instantaneous power, P $= F \cdot v$ .........(i) Since, $F = \text{pressure} \times \text{area}$ and pressure $= h_{\mathrm{Hg}} \cdot \rho_{\mathrm{Hg}} \cdot g$ Put these values in eq. (i), we get $P = h_{\mathrm{Hg}} \cdot \rho_{\mathrm{Hg}} \cdot g \cdot (A \cdot v)$ ........(ii) $=150 \times 10^{-3} \times 10^{3} \times 10 \times \frac{5 \times 10^{-3}}{60}$ $= \frac{(15) \times (136) \times (5)}{6} \times 10^{-3}$ $= 1700 \times 10^{-3} = 1.70\,\text{W}$