Lecture 4 PHY261 Circulatory System PDF

Lecture 4 PHY261 Faculty of Science Circulatory system Dr Ayman Sobhi Lecture Outline The Cardiovascular System Definition Function Blood circulation pathways Fluid motion BERNOULLI’S EQUATION VISCOSITY AND POISEUILLE’S LAW BLOOD PRESSURE when the body is horizontal or standing Effe...

Lecture 4 PHY261 Faculty of Science Circulatory system Dr Ayman Sobhi Lecture Outline The Cardiovascular System Definition Function Blood circulation pathways Fluid motion BERNOULLI’S EQUATION VISCOSITY AND POISEUILLE’S LAW BLOOD PRESSURE when the body is horizontal or standing Effect of acceleration on Blood pressure TURBULENT FLOW For viewing only Schematic diagram showing various routes of the circulation. For viewing only The Cardiovascular System Definition - A closed system of the heart and blood vessels - The heart pumps blood - Blood vessels allow blood to circulate to all parts of the body Blood is not a simple fluid; it contains cells that complicate the flow, especially when the passages become narrow. Function The blood in the circulatory system brings oxygen, nutrients, and various other vital substances to the cells and removes the metabolic waste products from the cells. The blood is pumped through the circulatory system by the heart, and it leaves the heart through vessels called arteries ‫ اﻟﺷراﯾﯾن‬and returns to it through veins ‫اﻷوردة‬. The Cardiovascular System Fluid motion L. M. Poiseuille (1799–1869), was a French physician whose study of moving fluids was motivated by his interest in the flow of blood through the body. In this lecture, we will review briefly the principles governing the flow of fluids and then examine the flow of blood in the circulatory system. Continuity equation Velocity 1 1 1 = 2 2 or 2 = 1 2 Cross-sectional area V capillary A capillary V Aorta A Aorta N=1 aorta M=2 V capillary A capillary N A aorta V aorta = M A capillaries V capillaries BERNOULLI’S EQUATION Bernoulli’s equation follows from the law of energy conservation. Because the three terms in the equation represent the total energy in the fluid, in the absence of friction their sum must remain constant no matter how the flow is altered. BERNOULLI’S EQUATION If frictional losses are neglected, the flow of an incompressible fluid is governed by Bernoulli’s equation, which gives the relationship between velocity, pressure, and elevation in a line of flow. Bernoulli’s equation states that at any point in the channel of a flowing fluid the following relationship holds: Pressure kinetic energy per unit volume 1 2 + ℎ+ = Constant 2 Potential energy per unit volume BERNOULLI’S EQUATION Pressure form of BERNOULLI’S EQUATION Static pressure Dynamic pressure Pressure kinetic energy per unit volume 1 2 + ℎ+ = Constant 2 Potential energy per unit volume Hydrostatic pressure BERNOULLI’S EQUATION BLOOD PRESSURE Foot Heart Brain when the body is horizontal If we have a person in the reclining (laying down) position, the measurement of blood pressure in the large arteries are almost the same everywhere. Analyze Using Bernoulli’s Equation  The velocities in the three main arteries (Brain, heart, and feet) are small, so that the term / ^ can be ignored.  Furthermore, in this position also the height of the brain, heart and feet are almost equal, so that the term ρ g y can be ignored from the formula. 1 2 1 2 1 2 + ℎ + = + ℎ + = Bℎ + ℎBℎ + ℎ B 2 2 2 = = ℎ the average arterial pressure is approximately constant throughout the body. BLOOD PRESSURE If a person is standing Using Bernoulli’s Equation  In the standing position, the situation is different, where only the term / ^ can be ignored and the term h has a significant effect.  Furthermore, in this position also the height of the brain, heart and feet are not equal, and the term h has a significant effect. 1 2 1 2 1 2 + ℎ + = + ℎ + = + ℎBℎ + 2 2 Bℎ 2 ℎ B + ℎ = = B ℎ + ℎℎB Example (1) When a 1.7 tall woman stands, her brain is 0.5 above her heart. If she bends so that her brain is 0.4 m below her heart, by how much does the blood pressure in her brain changes? the blood pressure at the heart is =13.3 x 103Pa, and take the blood density to be 1060 kgm-3 Solution For a standing person (13.3 x 10 Pa) + (1060 kgm-3 ) (10 n/m2) (1.2 m) = (PB) + (1060 kgm-3 ) (10 n/m2) (1.7 m) standing (PB) = 8 x 103 Pa For a Bending person (PB) = (13.3 x 10 Pa) + (1060 kgm-3 ) (10 n/m2) (0.4 m) Bending (PB) = 17.54 x 103 Pa 17.54 x 103 Pa - 8x 103 Pa = 9.54x 103 Pa Effect of acceleration on Blood pressure Effect of acceleration on Blood pressure A-upward acceleration For standing person Upward acceleration: If a man experience upward acceleration , then his effective weight becomes ( + ). PB + ρ (g+a) hB =PH + ρ (g+a) hH PB = PH - ρ (g+a) (hB -hH) As a increases PB decreases elevator Effect of acceleration on Blood pressure A-upward acceleration At certain value of a , the human will loose consciousness because the collapse of the arteries in the brain when the blood pressure at the brain equal zero PB = Zero Zero = PH - ρ (g+a) (hB -hH) ρ (g+a) (hB -hH) = PH elevator The Cardiovascular System Brain Effect of acceleration on Blood pressure A-upward acceleration Heart Effect of acceleration on Blood pressure Brain A-upward acceleration (hB -hH) = 0.4 m Heart 13300 pa (g+a) = PH= 13300 pa (1060 g/cm3) (0.4 m ) ρ = 1060 g/cm3 (g+a) = 32 m/sec2 = 3.2 x 10 = 3.2 g So, the value of the upward acceleration causing consciousness is 2.2 g Effect of acceleration on Blood pressure P What will the effect of the upward acceleration on the foot pressure f ? Homework Calculate the foot pressure for standing person Calculate the foot pressure for standing person in elevator with acceleration a PH= 13300 pa ρ = 1060 g/cm3 Pf Effect of acceleration on Blood pressure A-downward acceleration For standing person If a man experience downward acceleration , then his effective weight becomes ( - ). PB + ρ (g-a) hB =PH + ρ (g-a) hH elevator PB = PH - ρ (g-a) (hB -hH) As a increases PB decreases The Cardiovascular System Brain Effect of acceleration on Blood pressure (hB -hH) = 0.4 m B-downward acceleration What will the effect of the upward acceleration on Heart the foot pressure ? Pf Calculate the foot pressure for standing person Calculate the foot pressure for standing person in an elevator with acceleration a PH= 13300 pa ρ = 1060 g/cm3 Homework Example (2) A 1.8 m tall man stand in an elevator accelerating upward at 12 ms-2, what is the blood pressure in the brain and foot. Take the height difference between the heart and the brain to be 0.35 m? Solution PB + ρ (g+a) hB =PH + ρ (g+a) hH a=12 ms-2 PB = PH - ρ (g+a) (hB -hH) Brain PB = 13300 - 1060 (10+12) (0.35) (hB -hH) = 0.35 m Heart PB = 51400 pa 1.8 m PH= 13300 pa ρ = 1060 g/cm3 Calculate the foot pressure for standing person in an elevator with acceleration a The Cardiovascular System VISCOSITY AND POISEUILLE’S LAW Frictionless flow is an idealization. In a real fluid, the molecules attract each other; consequently, relative motion between the fluid molecules is opposed by a frictional force, which is called viscous friction. The Cardiovascular System VISCOSITY AND POISEUILLE’S LAW the rate of laminar flow Q through a cylindrical tube of radius r and length L is given by Poiseuille’s law, which is P1 P2 Q R 8ηL R π r4 The Cardiovascular System TURBULENT FLOW If the velocity of a fluid is increased past a critical point, the smooth laminar flow shown in is disrupted. The flow becomes turbulent with eddies and whirls disrupting the laminar flow The Cardiovascular System TURBULENT FLOW In a cylindrical pipe the critical flow velocity vc above which the flow is turbulent, is given by the Reynold’s number Viscosity of the fluid = diameter of the cylinder density of the fluid The frictional forces in turbulent flow are greater than in laminar flow. Therefore, as the flow turns turbulent, it becomes more difficult to force a fluid through a pipe. The Cardiovascular System TURBULENT FLOW the Reynold’s number Less than 2000 Laminar flow R Between 2000-3000 Transition flow larger than 3000 Turbulent flow Ex Anemia low red blood cells Low value of R low viscosity