Question

The heart of a man pumps $5$ litres of blood through the arteries per minute at a pressure of $150 \,mm$ of mercury. If the density of mercury be $13.6 \times 10^3$ $kg/m^3$ and $g$ = $10\, m/s^2$ then the power

• A. 3
• B. 1.5
• C. 1.7
• D. 2.35

Answer 1

The Correct Option is C

To find the power exerted by the heart, we need to use the formula for mechanical power in terms of pressure and volumetric flow rate:

P = \frac{dW}{dt} = \frac{\Delta P \cdot Q}{\rho \cdot g}

where:

• \Delta P is the pressure difference in Pascals (Pa)
• Q is the volumetric flow rate in m^3/s
• \rho is the density of the fluid (in this case, blood)
• g is the acceleration due to gravity

Given:

• The heart pumps 5 liters of blood per minute.
• The pressure is 150 mm of mercury.
• The density of mercury is 13.6 \times 10^3 \, \text{kg/m}^3.
• Acceleration due to gravity, g = 10 \, \text{m/s}^2.

First, convert the pressure from mm of mercury to Pascals:

\Delta P = 150 \, \text{mmHg} \times \frac{13.6 \times 10^3 \, \text{kg/m}^3 \times 10 \, \text{m/s}^2}{1000} = 2040 \, \text{Pa}

Next, convert the flow rate from liters per minute to m^3/s:

5 \, \text{L/min} = \frac{5}{1000} \, \text{m}^3 \times \frac{1}{60} \, \text{min/s} = \frac{5}{60000} \, \text{m}^3/\text{s}

Now calculate the power:

P = 2040 \, \text{Pa} \times \frac{5}{60000} \, \text{m}^3/\text{s} = 0.17 \, \text{W}

Hence, the power exerted by the heart is approximately 0.17 \, \text{W}, which is equal to 1.7 when expressing the result in the same order of magnitude as the other options.

Therefore, the correct answer is 1.7.