3 The device pumps the blood Into the aorta and then 1. (18 points) Forces in th
ID: 702817 • Letter: 3
Question
3 The device pumps the blood Into the aorta and then 1. (18 points) Forces in the body due to a left ventricular assist device (LVAD). A left ventricular assist device (LVAD) is a mechanical pump placed inside the body which helps pump blood from the left ventricle to the aorta, used when the left ventricle is weakened or failing. Suppose that 5 L/min of blood flow through the through the body. LVAD. Consider just the pump (not the tubes connecting from the ventricle to the aorta). The area at the entrance to the pump (right side of the diagram) is 12 cm², and the area at the exit is 28 cm3. Assume the density of blood is 1.0 g/cm3 or 1000 kg/m3. (Note that 1 L = 1000 cm3 = 0.001 m3). LEFT VENTRICLE O Blood enters the device from the ventricle Suppose that the pump is oriented horizontally, so that both input and output to the pump is along the x-axis shown in the diagram. The pressure of blood into the pump is 10 mmHg (=1333 Pa), and the pressure of blood out of the pump is 100 mmHg (=13,332 Pa). 2 A rotor inside the pump creates a continuous flow of bload. (a) What are the pressure forces (magnitude and direction) at the entrance (labelled 1) and exit (labelled 2) to the pump? PUMP flow (b) What is the horizontal (x-direction) force exerted on the pump by the body (in other words, the reaction force on the pump)? 600AExplanation / Answer
(a) area at entrance A1 = 12 cm2 = 0.0012 m2 (10000 cm2 = 1 m2)
Pressure at the entrance P1 = 1333 Pa
force at the entrance= A1*P1 = 0.0012 * 1333 = 1.5996 N (N= newton) direction = negative x direction horizontal
area at exit A2 = 28 cm2 = 0.0028 m2 (10000 cm2 = 1 m2)
Pressure at the exit P2 = 13332 Pa
force at the exit = A2*P2 = 0.0028 * 13332 = 37.32 N (N= newton) direction = negative x direction horizontal
(b) Horizontal force on the body = F2 - F1 = 37.32 - 1.5596 = 30.765 N reaction of body on the pump
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