Fluid Dynamics (Physics) Part 3 PDF

‫‪Physics‬‬ ‫‪fluid dynamics‬‬ ‫‪Part – 3‬‬ ‫ما تنسوش تتابعونا على‬ ‫تطبيق البشير‬ Fluids Fluids refer to all substances that can flow such as liquids and gases. Ideal Fluid: it is the medium that does not resist any shear stress, that is the layers of the...

‫‪Physics‬‬ ‫‪fluid dynamics‬‬ ‫‪Part – 3‬‬ ‫ما تنسوش تتابعونا على‬ ‫تطبيق البشير‬ Fluids Fluids refer to all substances that can flow such as liquids and gases. Ideal Fluid: it is the medium that does not resist any shear stress, that is the layers of the ideal fluid do not exert any friction forces between them. Laminar flow: type of fluid flow in which the fluid travels smoothly or in regular paths. Turbulent flow: type of fluid flow in which the fluid undergoes irregular fluctuations and mixing. Continuity Equation A1 V1 = A2 V2 The continuity equation states that the rate at which mass enters a system is equal to the rate at which mass leaves the system. Bernoulli's Equation: One of the important equations that used to analyze fluids motion is Bernoulli's Equation. 𝟏 𝑷𝟏 + 𝝆𝒈𝒉 + 𝝆𝒗2 = Const. 𝟐 DR. SHAMS 01002200666 Bernoulli's Equation: states that the total energy per unit volume at any point in the pipe in the case of smooth flow is always the same. Special cases of Bernoulli's Equation: 1) If the fluid is not in motion or if the flow is nearly steady (𝒗𝟏 = 𝒗𝟐) so the equation becomes P1 + 𝝆gh1 = P2 + 𝝆gh2 (hydrostatics) 2) If the flow is at constant height (horizontal pipe, h1 =h2) so the equation becomes 𝟏 𝟏 P1 + 𝒑𝒗𝟐𝟏 = P2 + 𝒑𝒗𝟐𝟐 𝟐 𝟐 Torricelli’s law: Torricelli’s Equation: is used for calculating the velocity of the liquid just as it leaves any hole Torricelli’s law, state that the speed V of fluid flowing out of an orifice in a tank under the force of gravity is proportional to the square root of the vertical distance h between the liquid surface and the center of the orifice and to the square root of twice the acceleration caused by gravity. v = √𝟐𝒈 (𝒉𝟐 − 𝒉𝟏 ) v = √𝟐 𝒈𝒉 The viscous flow of fluids: Viscosity refers to the resistance of a fluid to flow. The coefficient of viscosity: is the degree to which a fluid resists flow under an applied forces. FαA F α V/L Where A is the area of the plate and (V/L) is the velocity gradient DR. SHAMS 01002200666  𝑨𝑽 Torricelli’s law: F=𝜼 The greater the coefficient of viscosity η, the greater 𝑳 F : is the force required to move the layer. the force required to move the plate at a velocity v. V : is the velocity. A : is the surface area of the layer. L : is the distance between the top and bottom layers. η : is the coefficient of viscosity. Units of the viscosity coefficient: In MKS system: N / m2 = Pa. s In CGS system: poise (1 poise = 1dyne sec/cm2 ). Reynolds Number: Reynolds number is an important quantity in fluid mechanics used to help in predict flow patterns in different fluid flow situations. Reynolds Number: ⍴𝑫𝑽 𝑹= 𝛈 𝝆: is the density of the fluid. D: is the diameter of the pipe. 𝜼 : is the viscosity coefficient. 𝑽 : is the average flow velocity. R: is a dimensionless number  If R less than about 2000 ⟶ The flow of the fluid through the pipe is laminar flow.  If R greater than about 3000 ⟶ The flow of the fluid through the pipe is turbulent flow.  If R between 2000 and 3000 ⟶ is a transition region in which the flow is unstable. DR. SHAMS 01002200666  Examples Example (1): Water is flowing in a fire hose with a velocity of 1.0 m/s and a pressure of 200000 Pa. At the nozzle the pressure decreases to atmospheric pressure(101300 Pa), there is no change in height. Use the Bernoulli equation to calculate the velocity of the water exiting the nozzle. (Hint: The density of water is 1000 kg/m3). Solution Example (2): (a) Suppose that water at 20 c̊ flows with a velocity 20 cm/s through a pipe whose radius is 1 cm. Is the flow laminar or turbulent? (b) If we substitute air (also at 20 ̊c) for water in section (a), will the flow be laminar or turbulent? (a) For water The flow is turbulent DR. SHAMS 01002200666  Bioscience Essay The flow of blood in the circulatory system: The blood functions: 1) The blood supplies food and oxygen to the tissues of the body. 2) The blood carries away the waste products from the cells. 3) It distributes the heat generated by the cells to equalized the temperature of the body. 4) It carries the hormones that coordinate the activity of organs. 5) The blood distributes antibodies to fight infection. Blood Flow in the circulatory system:  Blood is a viscous fluid that is pumped through a complicated system of arteries and veins by muscular action of the heart.  The rate of flow of blood through the body is sufficiently small that the flow is generally laminar instead of turbulent.  The velocity of the blood flow is zero at arterial wall and flows most rapidly at the center of the artery.  The velocity of flow of a fluid as a function of the distance r from the center of a pipe given by 𝒂: is the inner radius of the pipe. 𝜼 : is the viscosity coefficient. 𝒍 : is length across which a pressure difference (𝑷𝟏 − 𝑷𝟐) exist. (𝑷𝟏 – 𝑷𝟐) : is the pressure differential between the ends of the pipe. 𝒎𝟑 The rate of flow Q in is given by Poiseuille’s law 𝒔 DR. SHAMS 01002200666 How can the pressure of blood in arteries be measured? The main artery in the upper arm chosen for the measurement. An inflatable strap is placed around the arm. The strap is then pumped up with air to pressure sufficient to collapse the artery and stop all flow. The valve on the strap is then opened and the air pressure is allowed to decrease slowly. The operator listens with the stethoscope ‫ السماعة‬placed down the artery downstream from the strap. The pressure in the strap at the first sound is recorded as the systolic pressure (120 torr) The pressure in the strap when the sound of turbulent flow ceases is recorded as the diastolic pressure )80 torr). DR. SHAMS 01002200666