7.26) A. Calculate the pressure (in N/m^2) that must be supplied by the "muscle pump" to create a pressure equivalent to 150 cm of blood. The density of blood is 1.05 g/cm^3. B. Calculate the wall tension "y" that must be created in the vessel by muscle action to produce this pressure. The radius of the vessel is 0.20 cm.
Note: Provide me an answer with solution/formula. Thanks!
To calculate the pressure that must be supplied by the "muscle pump" to create a pressure equivalent to 150 cm of blood, we can use the hydrostatic pressure formula:
Pressure = density × gravity × height
where:
Pressure is the pressure to be calculated
density is the density of blood
gravity is the acceleration due to gravity
height is the height of the blood column
Given:
density of blood = 1.05 g/cm^3
height = 150 cm
We need to convert the density to kg/m^3 and height to meters:
Density = 1.05 g/cm^3 = 1050 kg/m^3
Height = 150 cm = 1.5 meters
Now we can substitute the values into the formula:
Pressure = 1050 kg/m^3 × 9.8 m/s^2 × 1.5 meters
= 15435 N/m^2 (rounded to the nearest whole number)
Therefore, the pressure that must be supplied by the "muscle pump" is approximately 15435 N/m^2.
To calculate the wall tension "y" that must be created in the vessel by muscle action to produce this pressure, we can use the law of Laplace:
Tension = Pressure × radius
where:
Tension is the wall tension to be calculated
Pressure is the pressure we calculated earlier
Radius is the radius of the vessel
Given:
Pressure = 15435 N/m^2
Radius = 0.20 cm = 0.002 meters (converting cm to meters)
Now we can substitute the values into the formula:
Tension = 15435 N/m^2 × 0.002 meters
= 30.87 N (rounded to two decimal places)
Therefore, the wall tension "y" that must be created in the vessel by muscle action to produce the pressure is approximately 30.87 N.