The average human heart forces four litre of blood per minute through arteries a pressure of 125 mm. If the density of blood is `1.03xx10^(3)kg//m^(3)` then the power of heart is :

Options

A. `112.76xx10^(-6) HP`
B. 112.76 HP
C. `1.03xx10^(3)HP`
D. `1.03xx10^(-6)HP`

Answer

To find the power of the human heart based on the given parameters, we can follow these steps:

### Step 1: Convert the pressure from mmHg to Pascals
The pressure \( P \) is given as 125 mmHg. To convert this to Pascals, we use the conversion factor:
\[ 1 \text{ mmHg} = 133.322 \text{ Pa} \]
Thus,
\[ P = 125 \text{ mmHg} \times 133.322 \text{ Pa/mmHg} = 16665.25 \text{ Pa} \]

### Step 2: Convert the volume flow rate from liters per minute to cubic meters per second
The volume flow rate \( Q \) is given as 4 liters per minute. We convert this to cubic meters per second:
\[ Q = 4 \text{ liters/min} = 4 \times 10^{-3} \text{ m}^3/\text{min} \]
Since there are 60 seconds in a minute:
\[ Q = \frac{4 \times 10^{-3}}{60} \text{ m}^3/\text{s} = \frac{4}{60} \times 10^{-3} \text{ m}^3/\text{s} = \frac{1}{15} \times 10^{-3} \text{ m}^3/\text{s} \approx 6.67 \times 10^{-5} \text{ m}^3/\text{s} \]

### Step 3: Calculate the power using the formula
The power \( P_0 \) can be calculated using the formula:
\[ P_0 = P \times Q \]
Substituting the values we found:
\[ P_0 = 16665.25 \text{ Pa} \times 6.67 \times 10^{-5} \text{ m}^3/\text{s} \]
Calculating this gives:
\[ P_0 \approx 1.111 \text{ W} \]

### Step 4: Convert power from Watts to Horsepower
To convert power from Watts to Horsepower, we use the conversion:
\[ 1 \text{ HP} = 746 \text{ W} \]
Thus,
\[ P_0 \text{ (in HP)} = \frac{1.111 \text{ W}}{746 \text{ W/HP}} \approx 0.00149 \text{ HP} \]

### Final Answer
The power of the heart is approximately \( 0.00149 \text{ HP} \).

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