The human heart forces 4500 cc of blood/min through the arteries, under a pressure of 15 cm of Hg. Calculate the horsepower of the heart.Take 1 hp = 746 W and g = 980 cm/s2
First we will calculate the wattage of the heart and then convert it to hp (horsepower). A watt is a measure of power (work per unit time) and is defined by the SI units as `kg*m^2/s^3` , or kilogram meters squared per seconds cubed. The power of a pump such as the heart is found by multiplying the flow rate by the pressure. We are given both numbers in the question but we must first convert them to the proper units in order to get a watt upon multiplying.
The flow rate is given as 4500 cc/min. We need to convert this to `m^3/s` . Converting minutes to seconds is easy, we just multiply the number by 60 since there are 60 seconds per minute. Converting cubic centimeters to cubic meters is a little trickier. There are 100 cm in a meter but since we are dealing with a cubic length (raised to the third power) we must raise the factor of 100 to the third power. `100^3=1,000,000` . So we must divide the value of cm`^3` by 1,000,000 to get the m`^3` . This all is shown in the equation below:
`4500 cm^3/min (1 min/60 sec) (1 m^3/1,000,000 cm^3) = 0.000075 m^3/sec`
The pressure is given as 15 cm of Hg. We need to convert this number to `kg/(m*s^2)` , or a Pascal. We can use an online calculator to do this conversion directly and we get the `15 cm Hg = 19998.36 kg/(m*s^2).`
We can now multiply the flow rate by the pressure to get the power of the heart in watts:
`0.000075 m^3/s * 19998.36 kg/(m*s^2) = 1.50 kg*m^2/s^3 = 1.50 W`
Please note that all of the units work out to give a watt as the answer. Since there are 746 W per hp, simply divide the number by 746 to get the hp:
`1.50 W (1 hp/746 W) = 0.002 hp`
The final answer is 0.002 horsepower.