The heart of a man pumps 5 litres of blood through the arteries per mi...
Calculation of Power of Heart
Given:
- Volume of blood pumped by heart per minute (Q) = 5 litres = 0.005 m^3/min
- Pressure of blood pumped by heart (P) = 150 mm of mercury
- Density of mercury (ρ) = 13.6×10^3 kg/m^3
- Acceleration due to gravity (g) = 10 m/s^2
Conversion:
- 1 litre = 0.001 m^3
- 150 mm of mercury = 150/760 m of water (since 1 atm = 760 mm of mercury) = 0.197 atm
- 1 atm = 101325 Pa (Pascal)
- 1 Pa = 1 N/m^2
- 1 W (Watt) = 1 J/s (Joule per second)
Calculation:
- Pressure of blood in Pa = 0.197 atm x 101325 Pa/atm = 19999.425 Pa
- Force exerted by heart (F) = Q x P = 0.005 m^3/min x 19999.425 Pa = 99.997125 N/min
- Work done by heart (W) = F x d = m x g x d = ρ x V x g x d (since m = ρ x V)
- Here, d is the distance travelled by the blood in one minute, which is equal to the length of the circulatory system (about 100,000 km)
- Therefore, d = 100,000 km = 100,000,000 m
- W = ρ x V x g x d = 13.6×10^3 kg/m^3 x 0.005 m^3/min x 10 m/s^2 x 100,000,000 m = 6.8 x 10^9 J/min
- Power of heart (P) = W/t = 6.8 x 10^9 J/min / 60 s/min = 1.13 x 10^8 W
Therefore, the power of the heart is 1.13 x 10^8 W.
The heart of a man pumps 5 litres of blood through the arteries per mi...
Power=pressure×volume/time .
and pressure=dhg.
on calculation you will get ans. near to 1.7
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