1、Medical physics,Why should we study physics ? This is one of the questions most frequently asked by medical students ,It seems appropriate therefore to begin this book with an attempt to answer it .The physics is related to medicine and biological science mainly in two respects .The physical laws go
2、verning the behavior of molecules ,atoms and atomic nuclei one the basis for chemistry and biochemistry physiology offers many examples of physical processes and principles diffusion within cells the regulation of body temperature . The motion of fluids in the circulatory system and electrical signa
3、l in nerve fibers are just a few.The most obvious impact of physics on biology and medicine is at the level of instrumentation. (万物变化-物理规律、数学工具）,the Nobel prize related to physics,(usually we do not sayMechanics of fluids, but hydrodynamics),CHAPTER 4 THE MOTION OF FLUIDS,Hydrostatics (流体静力学),Hydros
4、tatics is the study of fluids at rest. Liquids flow under the action of unbalanced forces, so that if an amount of liquid is stationary, or static (静态的), the net force acting on the amount is zero. That is why it is named as hydrostatics.,Pressure and Pascals principle,Pressure is defined as the mag
5、nitude of the force per unit area. It is found that the hydrostatic pressure P at some point in liquid is P = F/A = g h(3.2),Density (密度),You have little trouble walking upstream against a 5 km/h current of air (气流). Fighting the same flow waist-deep of water requires considerable effort, while oppo
6、sing a similar current in a mudflow （泥浆流）is beyond your capacity. The distinction is mainly the DENSITY of fluid.The density of a homogeneous (均匀的）substance is defined as the mass of the material per unit volumewhere m is the mass of the object and V is its volume (体积).,Pascals principle:When a chan
7、ge in pressure is applied to an enclosed fluid, the change is transmitted undiminishedly (do not become smaller) to every point in the fluid and to the walls of the container.,According to Pascals principle, the pressure P1 at one end should be equal to P2 at another end. i.e P1 = P2,(3.4),Fig. 3.2
8、hydraulic pressure,A2,A1,Buoyancy (浮力) and Archimedes principle,A body immersed in a fluid is buoyed (使浮起) up by a force equal to the weight of fluid which the body has displaced.,Where V is the volume of fluid displaced by the body, is the density of the fluid and g is the gravitational acceleratio
9、n. This is called Archimedes principle. (A story describes about how Archimede got his principle. It is said that the king in his country asked him to find a method to distinguish whether the gold is pure. He worked out this problem while he was taking his bath. He was so excited that he did not rea
10、lize that he was naked when he ran on the street to tell the good news to his king.),Main knowledge,1. To master Equation of continuity, Bernoulli equation , Poiseuille principle，the application of Bernoulli equation；To understand ideal fluid ,viscous fluid, steady flow, laminar flow, turbulent flow
11、 ,viscosity etc. To know heart works 。,CHAPTER 4 THE MOTION OF FLUIDS,Section 1 Ideal fluid equation of continuity,Section 2 Bernoulli equation,Section 3,Section 4 The law of Viscous fluid flow,CHAPTER 4 THE MOTION OF FLUIDS,Viscous fluid flow,. Ideal fluid,Section 1 Ideal fluid equation of continui
12、ty,. Steady flow,. Equation of continuity,Fluid is the general name for gases and liquids. It has no definite size and shape unless it is hold in a container.The difference between solid and fluid is that the molecules (or atoms) in liquids can move in a large area or even from one place to another
13、and those in solids can only vibrate in a very small range.The distinction between gases and liquids is that they differ to a great degree in compressibility (可压缩性). Gases may be compressed with ease, while liquids are practically incompressible.,流体流动的描述方法,拉格朗日法: 对于流体的流动通常有两种不同的考察方法.一种方法是选定一个流体质点,对其
14、跟踪观察,描述其运动参数与时间的关系.此法描述的是同一质点在不同时刻的状态. 欧拉法: 它描述的则是空间各点的状态及其与时间的关系.此法并不跟踪流体质点进行观察,而是在固定位置上观察流体质点的运动情况.欧拉法系直接描述各有关运动参数在指定空间和时间上的变化.,In order to make the real problem simple, We use an ideal model to replace the real fluid. It is called ideal fluid. The ideal fluid has the following properties: non-vis
15、cous (no internal friction) (无粘性的) incompressible（不可压缩的） Moving in a streamline motion,Ideal fluid,二. Steady flow of ideal fluid,The velocity (pressure 、density )of every element passing through a given point doesnt change in both magnitude and direction .(although the velocity of a particular parti
16、cle of the fluid may change as it moves from one point to another),1. steady flow,The velocity at each point of space rains constant in time,Steady flow of ideal fluid,Velocity doesnt change ，magnitude and direction dont change，(pressure density),Not particles moving speed ，but fluids flowing speed
17、of space points,Dont require each point have the same velocity；,This is a moving state of ideal,理想液体的定常流动,Steady flow (Another description) : If the velocity of every point on the streamline does not change at different moment, this kind of fluid is called steady flow or streamline flow.,2. streamli
18、ne,2. streamline,Electric field line,Magnetic field line,In steady flow ,the streamlines coincide with the lines of flow, Streamline (流线): In the motion of fluid, the velocity of particles in the fluid may be different. At any given moment, we can draw some lines. The tangent direction of every poin
19、t on the line has the same direction as velocity. The lines are called streamlines. (It is also defined that a curve whose tangent, at any point, is in the direction of the fluid velocity at that point).,streamline,The fluid follows the path of streamline , streamline doesnt change an any moment.,St
20、reamlines cant cross at any point because each point has only one velocity,The tangent of a curve is in the direction of the fluid velocity at that point.,理想液体的定常流动,No streamlines can be crossed! (otherwise, the cross point will have two tangential lines.),3. Flow tube (tube of flow),理想液体的定常流动,a flo
21、w tube is bounded by streamlines. If we construct all of the streamlines passing through the periphery of an element of area ,such as the area S ,these lines enclose a tube called a flow tube or tube of flow,The movement-laws of fluid in a tube of flow represent whole the fluids movement .,From the
22、definition of a streamline,no fluids can cross the slide walls of a flow tube,As the pipe has different cross-sections in different places, the different places should have the different flow speed.,三、 continuity Equation,Flux: It represents volume flow rate which vertically passes through the secti
23、on per unit time.,Sv=Q( flux ),S1 n1 = S2 n2,volume flow rate (体积流量),S v = constant means that the Volume Flow Rate is conservative.,. Form of the equation,Section 2 Bernoullis equation and its application,. Eduction of the equation,. Applications of the equation,Now we need a method for calculating
24、 the velocity change that occurs when a fluid flows in a pipe of variable cross section. Consider an ideal fluid in streamline flow in a pipe of variable cross-section (横截面).,Pitot tube,A点为停滞点，vA= 0,三. Applications of the equation,S1 v1 = S2 v2,S2 small,v2 big,P2 small,the liquid is absorbed in the
25、high speed airflow and is sprayed in a state of fog,喷雾器的空吸原理,伯努利方程及其应用,三. The application of equation,3. Velocity at point 2,S1 v1 p1,S2 v2 p2,S1S2,p1 = p2 = p0,v1 o,伯努利方程及其应用,三. The application of equation,3. Velocity at point 2,伯努利方程及其应用,三. The applications of equation,4. The relation between pres
26、sure and height,Example:Blood pressure and bodys poise,心脏位置 13.33kPa （动脉压）,lying,heart,Head,foot,stand,13.33,13.33,12.67,12.67,6.8,24.40,伯努利方程及其应用,headstand,课外扩展解释现象-虹吸管,利用灌满液体的曲管将液体经过高出液面的地方引向低处,这种疏运液体的曲管称为虹吸管.,流速与高度的关系,选取液面A点和虹吸管流出口D点为参考点,返回,上述结果表明在压强不变的条件下,液流过程中重力势能与动能之间的转换关系,即液面与出口处的高度差越大,则出口的流速
27、越大.,返回,压强与流速的关系,选取A 、B两点为参考点,返回,上式表明在重力势能不变的前提下,液流过程中压强能与动能之间的转换关系,即流速越大处压强越小,流速越小处压强越大.,返回,压强与高度的关系,选取C、D为参考点,返回,上式表明流速不变时,液体流动过程中压强能与重力势能之间的转换关系,即处于高处液体的压强小于低处液体的压强.,返回,Summary to the last lecture,1. Continuity equation,Volume Flow Rate is conservative.,2. Bernoullis equation,3. Deductions (推论) fr
28、om Bernoullis equation Hydrostatics (v=0),This result could explain that the body position has some influence on the blood pressure. Horizontal pipe (h1 = h2 = 0),4. Applications of Bernoullis equation,Pitot tube,kinemometer,Special terms will be used in this lecture,Laminar flow (层流） transparent (透
29、明的, opaque); glycerol (甘油); gradient (速度梯度), stack (vt. 堆积起, 迭加(层) Turbulent flow (湍流); eddy (旋涡, eddies ) parameter (参数); coefficient of viscosity (粘性系数) friction (摩擦力); resistance (阻力) proportional to (正比于); vessel (脉管), artery (动脉) ; bronchi （支气管),Newtonian viscous law,Turbulent flow and laminar
30、flow,Section3. The flow of viscous (粘滞的) fluid,Reynolds number,The real fluid has internal friction and it is viscous. It is different from the ideal fluid. It wastes energy when it flows since internal friction does work in opposite direction. So Bernoullis equation can not explain the flow of visc
31、ous fluid. Some new concepts are required to be put forward.,The flow of viscous (粘滞的) fluid.,一. Newton viscous law,Experiment,actual fluids flow,一. Newton viscous law,when ideal fluid flows in an even tube ，the velocities at the same section are same；,1. Experiment -phenomenon,实际液体的流动,2. Actual flu
32、id flow,Put some transparent glycerol (甘油) in a tube and then put in some colored glycerol. Let them flow. From the colored glycerols shape change, we can see the flow velocity of glycerol is different in different places.,v=v(t),实际液体的流动,The speed is smaller near the wall of the tube and flow veloci
33、ty is the biggest in the center of the tube. This means that viscous fluid flows in different layers. We call it Laminar Flow. when fluid flows in laminar flow, there is internal friction or viscous force between two close layers.,The internal friction is caused by the interaction forces between mol
34、ecules. The internal friction is bigger in liquids than in gases.,phenomenon,In laminar flow, the fluids are imagined as being made up of very thin liquid layers stacked (堆叠) parallel to the surface across which flow occurs.,3. Viscosity (粘度) internal friction,Viscosity may be thought of as the inte
35、rnal friction of a fluid. Because of viscosity ,a force must be exerted to cause one layer of a fluid to slide past another. 粘滞力-viscous force,x - the distance changed between two layersv - the velocity changed between two layers The velocity change per unit length is the slope of the function v(x)
36、at point x. it is also called velocity gradient (速度梯度) in x-direction, expressed as,Velocity gradient-液体流动的速度梯度速度沿与速度垂直方向距离的变化率,4.Velocity gradient,较小,较大,Velocity gradient,Newton viscous law,实际液体的流动,5. Newton viscous law,Experiments show that on one hand if the velocity gradient (梯度,坡度) is large, th
37、e frictional force F is large as well; on the other hand, the greater the area of the two connected layers, the larger the frictional force. Therefore, the frictional force F is proportional to the area of the two connected layers and velocity gradient.,This equation is called Newtons law of viscosi
38、ty., contact with temperature, decrease with the temperatures increasing.,S: area of adjacent layers, : 液体的粘滞系数 、内磨擦系数、粘度:viscosity,Velocity gradient,Where is the coefficient (系数) of viscosity and determined by the nature and temperature of the fluid. It () is a measure (量度) of the frictional force
39、in liquids.,laminar flow and Turbulent flow,laminar flow,Because of the viscosity ,The fluids flow inDifferent layers , Each layer has the same speed as that surface.,Each layers slides past another layer ,but they dont complex each other各液层之间仅作相对滑动而不相互混合,When the velocity of fluid is bigger than so
40、me value, the flow is neither steady flow nor laminar flow and it is very irregular. The particles in fluid in out-layer is involved into the inner layer, moving in little eddies (旋涡). This flow is called turbulent flow.,Turbulent flow,when the speed increases to some value laminar flow is destroyed
41、 ,the particle element maybe flow at all the direction .,adjacent layer may be to complex each other 各层液体开始互相掺混，甚至出现湍旋,Re 2000,1000 Re PC PD PE PB,实际液体的流动,Proportional to the gauge pressure,A pressure gradient between the point and the end,二. Bernoullis equation of actual fluid,The energies of each
42、unit volume decrease from A to B (overcome friction克服内摩擦力作功),h1: pressure 提供克服内摩擦力所需的能量,h2: velocity 维持管中液流的速度,实际液体的流动,心脏做功(heart works),心脏做功等于左、右心室做功之和,整个心脏做功,一般正常人,Poiseulle law,When a fluid flows in a tube ,the flow velocity is different at different points of cross section .the outermost layer o
43、f fluid clings to the walls of the tube , and its velocity is zero .the tube walls exert a backward drag on this layer ,which in turn drags backward on the next layer beyond it , and so on .if the velocity is not too great ,the flow is laminar .with a velocity that is greatest at the center of the t
44、ube and decrease to zero at the walls,Lets consider the variation of velocity with radius for a cylindrical pipe of inner radius R .we consider the flow of a cylindrical element of fluid coaxial with the pipe of radius r and length L .as show in fig .,The relation between flux of fluid and parameters of tube, : velocity,p1 p2 : Pressure,L：length,R： raduis of tube,泊肃叶定律,Poiseuille law,泊肃叶定律,1Educe of Poiseuille law,The Net force :,Internal friction force of cylindrical surface or viscous force,Minus 负号表示 v随r的增大而减小,Steady fluid,泊肃叶定律,1Educe of Poiseuille law,
