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Transport engineering. thank you for your help! Problem 5. Bernoulli Equation Problem from Fournier Textbook Related to Blood Flow through Heart and Lungs. The cardiac
Transport engineering. thank you for your help!
Problem 5. Bernoulli Equation Problem from Fournier Textbook Related to Blood Flow through Heart and Lungs. The cardiac output of the adult human heart is normally around 5.0L/min. Blood enters the right atrium of the heart and is then pumped from the right ventricle to the lungs to exchange O2 and CO2. Blood then exits the lungs and flows back to the left atrium of the heart, with the left ventricle then pumping the blood to the rest of the body. Assume a situation with the following pressures under laminar-flow conditions (all pressures given as gage pressure). The blood enters the right atrium of the heart at a pressure of 0.0mmHg and exits the right ventricle of the heart via the pulmonary arteries under a pressure of 15.0mmHg and flows to the lungs. The blood then exits the lungs and returns to the left atrium of the heart via the pulmonary veins under a pressure of 6.0mmHg. Finally, the blood is pumped by the left ventricle of the heart under a pressure of 123.0mmHg to supply the body with oxygenated blood. Using the general form of the Bernoulli equation that includes pump work as presented in class (i.e., given in Fournier, not in Truskey), calculate the following values: (A) (5 pts) The total work performed by the heart (units: J/min ) to pump the blood under these conditions. (B) (5 pts) The frictional loss of the blood (units: J/min ) as it flows through the capillary beds of the lungs. For simplicity for this problem, you may assume =1,hf is negligible for flow through the heart and the blood vessels connecting the heart and lungs (i.e., hf=0 ), but not for the lungs themselves, and that you can neglect both kinetic energy ( v2 terms) and potential energy ( gz terms) differences-i.e., flow velocity is approximately equal for flow to and from the heart and lungs, and no appreciable difference in height for the inlets and outlets of these organs. Use a value for the density of the blood of 1.06g/cm3. Some helpful conversion factors: 1Watt=1Joule(J)/sec.1J=1Nm=kgm2/sec2
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