Power: Practice Problem & Solution
The heart of a man pumps $5\text{ litres}$ of blood through the arteries per minute at a pressure of $150\text{ mm}$ of mercury. If the density of mercury be $13.6 \times 10^3\text{ kg/m}^3$ and $g = 10\text{ m/s}^2$, then the power of heart in watt is: (2015 Re)
Solution Explained:
To solve this problem, we apply the core principles of Power. Understanding the underlying formula is key to arriving at the correct answer below:
Power is given by $P = p \left(\frac{dV}{dt}\right)$. Pressure $p = h\rho g = 0.15 \times 13.6 \times 10^3 \times 10 = 2.04 \times 10^4\text{ Pa}$. Volume flow rate $\frac{dV}{dt} = \frac{5 \times 10^{-3}}{60}\text{ m}^3\text{/s}$. Multiplying these gives $1.70\text{ W}$.
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