Fluid Mechanics Concepts PDF

1- Pressure 2- Fluid 3- Viscosity 4- surface Tension 5- Electricity Dr Karam Fathy Pressure - Pressure is defined as force per unit area. It is usually more convenient to use pressure rather than force to describe the influences upon fluid behavior. The standard unit for pressure is the Pascal, whi...

1- Pressure 2- Fluid 3- Viscosity 4- surface Tension 5- Electricity Dr Karam Fathy Pressure - Pressure is defined as force per unit area. It is usually more convenient to use pressure rather than force to describe the influences upon fluid behavior. The standard unit for pressure is the Pascal, which is a N/m2. - For an object sitting on a surface, the force pressing on the surface is the weight of the object, but in different orientations it might have a different area in contact with the surface and therefore exert a different pressure. Static Fluid Pressure - The pressure exerted by a static fluid depends only upon the depth of the fluid, the density of the fluid, and the acceleration of gravity. P static fluid = ρgh Where ρ is the density and = m/V g is the acceleration of gravity h is the depth of fluid - Because of the ease of visualizing a column height of a known liquid, it has become common practice to state all kinds of pressures in column Manometer - A device for measuring the pressure of a gas contained in a vessel - One end of the U-shaped tube is open to the atmosphere - The other end is connected to the pressure to be measured Pressure at B is P = P0+ρgh Buoyant Forces and Archimedes’s Principle - Consider a rectangular solid immersed in a fluid of uniform density ρ as illustrated in the figure. Let the top and the bottom surfaces have area A. The force on the lower face of the block is F2=P2A and the force on the upper face is F1=P1A.The total force on the block due to the fluid called the buoyant force FB. FB=(P2-P1)A Since P2-P1 = ρgd, the magnitude of the buoyant force can be written FB = ρ g dA = ρ gV Where V=Ad is the volume of the block. Archimedes' principle: A fluid exerts an upward buoyant force on a submerged object equal in magnitude to the weight of the volume of the fluid displaced by the object. It acts upward through the centroid of the displaced volume. FB = weight of displaced liquid = W = ρliq Vimirsied g 1. ρ body< ρ fluid: Floating body 2. ρ body= ρ fluid: Neutrally buoyant 3. ρ body> ρ fluid: Sinking Body Viscosity Viscosity is the internal friction of a fluid. is the measure of its resistance to gradual deformation by shear stress or tensile stress - If the flow of a fluid is smooth, it is called streamline or laminar flow (a). - Above a certain speed, the flow becomes turbulent (b). - The highest velocity (Vmax) is found in the center of the vessel.The lowest velocity (V=0) is found along the vessel wall.  𝑠h𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠 𝑭/𝑨 𝜼= = 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐h𝑎𝑛𝑔𝑒 𝑜𝑓 𝑠h𝑒𝑎𝑟 𝑠𝑡𝑟𝑎𝑖𝑛 𝒗/𝒍 The unit of viscosity in the SI units is 1N.S/m2, while the corresponding CGS unit is 1 dyn.s/cm2. The common unit of viscosity is 1 poise. 1 poise = 1 dyn.s/cm2= 10-1N.s/m2 Small viscosities are expressed in centipoises (1 cp= 10-2) or micropoises (1μ= 10-6). Fluid The mass flow rate is the mass that passes a given point per unit time. The flow rates at any two points must be equal, as long as no fluid is being added or taken away. This gives us the equation of continuity: If the density doesn’t change – typical for liquids – this simplifies to. Where the pipe is wider, the flow is slower. AV = a1v1 + a2v2 + a3v3 Fluid under conditions of high flow, particularly in the ascending aorta, laminar flow can be disrupted and become turbulent. When this occurs, blood does not flow linearly and smoothly in adjacent layers, but instead the flow can be described as being chaotic. Turbulent flow also occurs in large arteries at branch points, in diseased and narrowed (stenotic) arteries (see figure below), and across stenotic heart valves Surface Tension Surface tension is the elastic tendency of a fluid surface which makes it acquire the least surface area possible. Surface tension allows insects (e.g. water striders), usually denser than water, to float and stride on a water surface. At liquid–air interfaces surface tension results from the greater attraction of liquid molecules to each other (due to cohesion) than to the molecules in the air (due to adhesion) Surface Tension and Bubbles The surface tension of water provides the necessary wall tension for the formation of bubbles with water. The tendency to minimize that wall tension pulls the bubbles into spherical shapes. Consider an air bubble of radius r as shown in the Figure. The external pressure is Po and the internal pressure is P1. The force to the pressure difference is 𝑭𝑷 = 𝑷𝟏 − 𝑷𝒐 𝝅𝒓𝟐 The force from surface tension is 𝑭𝜸 = 𝜸 𝟐𝝅𝒓 The pressure difference is 𝟐𝜸 𝚫𝑷 = 𝒓 This is known as Laplace's law for a spherical membrane for an air bubble The Cardiovascular System The cardiovascular system is sometimes called the blood- vascular, or simply the circulatory, system. It consists of the heart, which is a muscular pumping device, and a closed system of vessels called arteries, veins, and capillaries. In this system, blood is pumped by the heart around a closed circle or circuit of vessels as it passes again and again through the various "circulations" of the body. The Cardiovascular System The vital role of the cardiovascular system in maintaining homeostasis depends on the continuous and controlled movement of blood through the thousands of miles of capillaries that permeate every tissue and reach every cell in the body. Nutrients and other essential materials pass from capillary blood into fluids surrounding the cells as waste products are removed. In the cardiovascular system, there are control mechanisms that work to organize and integrate the various functions and components of this system to supply blood to specific areas of the body as needed. It also ensures a stable internal environment surrounding every cell of the body, regardless of the difference in demand for nutrients or production of waste. The Cardiovascular System Blood: 1. components 2. blood pressure 3. viscosity Vessels: 1. arteries 2. veins 3. capillaries 4. continuity equation Heart: 1. construction 2. neuron cell 3. Muscle contraction and relaxation 4. ECG Lungs: 1. Alveoli 2. surfactant 3. gas exchange  Blood Blood is a fluid that moves through the vessels of a circulatory system. In humans, it includes plasma (the liquid portion), blood cells (which come in both red and white varieties), and cell fragments called platelets.  Blood 1. Plasma ❖ The liquid component of blood, can be isolated by spinning a tube of whole blood at high speeds in a centrifuge. ❖ Plasma accounts for around 55% of blood fluid in humans. Plasma is 92% water, and the contents of the remaining 8% include: 1. Glucose 2. Hormones 3. Proteins 4. mineral salts 5. Fats 6. vitamins ❖ The main job of the plasma is to transport blood cells throughout your body along with nutrients, waste products, antibodies, clotting proteins, chemical messengers such as hormones, and proteins that help maintain the body's fluid balance  Blood 2. Red Blood Cells (erythrocytes) ❖ They are specialized cells that circulate through the body and deliver oxygen to tissues. ❖ In humans, red blood cells are small and biconcave (about 100 μm3), and do not contain mitochondria or a nucleus when mature. ❖ These characteristics allow red blood cells to effectively perform their task of oxygen transport. ❖ Small size and biconcave shape increase the surface area-to-volume ratio, improving gas exchange, while lack of a nucleus makes additional space for hemoglobin, a key protein used in oxygen transport.  Blood 2. Red Blood Cells (erythrocytes) ❖ Lack of mitochondria keeps red blood cells from using any of the oxygen they’re carrying, maximizing the amount delivered to tissues of the body. ❖ Red blood cells also play an important role in transport of carbon dioxide, a waste product, from the tissues back to the lungs. ❖ Red blood cells have an average life span of 120 days. ❖ Old or damaged red blood cells are broken down in the liver and spleen, and new ones are produced in the bone marrow. ❖ Red blood cell production is controlled by the hormone erythropoietin, which is released by the kidneys in response to low oxygen levels to ensure that the number of cells in the body remains relatively constant over time.  Blood 3. White Blood Cells (leukocytes) ❖ White blood cells are an important part of your immune system. Your immune system detects and deals with infections or foreign molecules that enter your body. Things that cause infection are called pathogens (germs). ❖ The main types of white blood cells are: 1. Neutrophils: the most common type of white blood cell, and the first cell to respond to an infection. They move to infected areas of your body to engulf and destroy germs such as ; bacteria, fungi, and viruses. 2. Monocytes: play a similar role to the neutrophils. They also help your lymphocytes to produce antibodies 3. Eosinophils and Basophils: Eosinophils and basophils help your body fight infections, particularly those caused by parasites. They also pay a role in allergic reactions. 4. Lymphocytes: Lymphocytes control the way your other immune cell's function.  Blood 4. Platelets (thrombocytes) ❖ Unlike red and white blood cells, platelets are not actually cells but rather small fragments of cells. ❖ Platelets help the blood clotting process (or coagulation) by gathering at the site of an injury, sticking to the lining of the injured blood vessel, and forming a platform on which blood coagulation can occur. ❖ This results in the formation of a fibrin clot, which covers the wound and prevents blood from leaking out. Fibrin also forms the initial scaffolding upon which new tissue forms, thus promoting healing. ❖ A higher-than-normal number of platelets can cause unnecessary clotting, which can lead to strokes and heart attacks. Therefore, treatments that help prevent these potentially fatal events are needed to reduce the counts can of them. Blood Pressure - The systolic pressure is the maximum pressure in an artery at the moment when the heart is beating and pumping blood through the body. - The diastolic pressure is the lowest pressure in an artery in the moments between beats when the heart is resting. Both the systolic and diastolic pressure measurements are important - if either one is raised, it means you have high blood pressure (hypertension ) Fluid Vascular Network VESSEL TYPE DIAMETER (mm) FUNCTION Pulse dampening and Aorta 25 distribution Large Arteries 1.0 - 4.0 Distribution of arterial blood Small Arteries 0.2 - 1.0 Distribution and resistance Resistance (pressure & flow Arterioles 0.01 - 0.20 regulation) Capillaries 0.006 - 0.010 Exchange Exchange, collection, and Venules 0.01 - 0.20 capacitance Capacitance function (blood Veins 0.2 - 5.0 volume) Vena Cava 35 Collection of venous blood How many cubic meters of blood does the heart pump in a 70-year lifetime, assuming the average flow rate is 5.00 L/min? The aorta is the principal blood vessel through which blood leaves the heart in order to circulate around the body. (a) Calculate the average speed of the blood in the aorta if the flow rate is 5.0 L/min. The aorta has a radius of 10 mm. (b) Blood also flows through smaller blood vessels known as capillaries. If the average number of capillaries is about 5 billion, the rate of blood flow in the aorta is 5.0 L/min, and the average diameter of a capillary is 8.0 μm, calculate the speed of blood in the capillaries. (c) Calculate the average number of capillaries in each gram of a human whose mass is about 70 kg?