7.27) Under extreme circumstances total flow rate in the circulatory system may reach 38 liters/min, (633 cm^3/sec). A. Calculate the kinetic power output of the left ventricle if the average blood velocity is consequently 230 cm/sec and the density of the blood is 1.05 g/cm^3. B. Calculate the pressure power output of the left ventricle if the average pressure is 150 mm Hg.
Note: Please provide me an answer with solution/formula. Thanks!
A. To calculate the kinetic power output of the left ventricle, we need to use the formula:
Power = (1/2) * mass flow rate * velocity^2
First, we need to convert the flow rate from cm^3/sec to liters/min:
38 liters/min = 38000 cm^3/min
Therefore, the mass flow rate can be calculated as follows:
mass flow rate = density * volume flow rate
= (1.05 g/cm^3) * (633 cm^3/sec)
= 666.15 g/sec
Now we can substitute the values into the power formula:
Power = (1/2) * (666.15 g/sec) * (230 cm/sec)^2
Simplifying the equation, we get:
Power = (1/2) * 666.15 * (230)^2
= (1/2) * 666.15 * 52900
= 17605882.75 g * cm^2/sec^3
B. To calculate the pressure power output of the left ventricle, we can use the formula:
Power = flow rate * pressure difference
First, we need to convert the pressure from mm Hg to cm H2O:
1 mm Hg = 1.36 cm H2O
Therefore, the average pressure can be calculated as follows:
average pressure = (150 mm Hg) * (1.36 cm H2O/mm Hg)
= 204 cm H2O
Now we can substitute the values into the power formula:
Power = (633 cm^3/sec) * (204 cm H2O)
= 129132 cm^3 * cm H2O/sec
Please note that the units of power in both cases are different. In part A, the power is in g * cm^2/sec^3, and in part B, the power is in cm^3 * cm H2O/sec.
Hope this helps!