Fluid Dynamics Lecture 5 PDF

Lect. 5 Fluid Dynamics Asst. Prof. M.A. Abdo Laminar and turbulent flow Turbulent Flow ⚫ An irregular flow characterized by small whirlpool-like regions ⚫ Turbulent flow occurs when the particles go above some critical speed Laminar Flow ⚫ Steady flow ⚫ Each particle of the flui...

Lect. 5 Fluid Dynamics Asst. Prof. M.A. Abdo Laminar and turbulent flow Turbulent Flow ⚫ An irregular flow characterized by small whirlpool-like regions ⚫ Turbulent flow occurs when the particles go above some critical speed Laminar Flow ⚫ Steady flow ⚫ Each particle of the fluid follows a smooth path ⚫ The paths of the different particles never cross each other ⚫ The path taken by the particles is called a streamline Streamlines ⚫ The path the particle takes in steady flow is a streamline ⚫ The velocity of the particle is tangent to the streamline ⚫ A set of streamlines is called a tube of flow Equation of Continuity ⚫ Consider a fluid moving through a pipe of nonuniform size (diameter) ⚫ The particles move along streamlines in steady flow ⚫ The mass that crosses A1 in some time interval is the same as the mass that crosses A2 in that same time interval ⚫ m1 = m2 or ρV1 = ρV2 ⚫ ρA1Δx1 = ρ A2Δx2 ⚫ ρ A1 v1Δt = ρ A2v2Δt ⚫ A1v1 = A2v2 ⚫ A1v1 = A2v2 This is called the equation of continuity for fluids The product of the area and the fluid speed at all points along a pipe is constant for an incompressible fluid Equation of Continuity A1v1 = A2v2= constant ⚫The speed is high where the tube is small (small A) ⚫The speed is low where the tube is wide (large A)  Daniel Bernoulli ⚫ 1700 – 1782 ⚫ Swiss physicist ⚫ Published Hydrodynamica ⚫ Dealt with equilibrium, pressure and speeds in fluids ⚫ Also a beginning of the study of gasses with changing pressure and temperature The force exerted by the fluid to the left of the blue portion in has a magnitude F1= P1A1. The work done by this force on the segment in a time interval Δt is W1 = F1 Δx1 = P1A1 Δx1 = P1V1, where V is the volume of the blue portion of fluid passing point 1. In a similar manner, the work done by the fluid to the right of the segment in the same time interval Δt is W2 = -F2 Δx2 -P2A2Δx2 = -P2V2, where V2 is the volume of the blue portion of fluid passing point 2. This work is negative because the force on the segment of fluid is to the left (inside). The volumes of the blue portions of fluid in this Figure are equal because the fluid is incompressible ) V1=V2, Hence W1 = P1V and W2 = P2V Therefore, the net work done (W) on the segment by these forces in the time interval Δt is: W= W1- W2 = P1 V -P2 V W= (P1-P2)V This work is responsible for the movement of fluid This net work done is equal to the change in mechanical energy of the system: W = ΔK + ΔU ΔK is the change in the kinetic energy ΔU is the change in the potential energy m is the mass of the blue portions of fluid in both parts  W = (P1-P2)V = ΔK + ΔU Bernoulli’s equation shows that the pressure of a fluid decreases as the speed of the fluid increases. In addition, the pressure decreases as the elevation increases Applications of Fluid Dynamics As the speed increases, the pressure decreases Bernoulli’s Equation, Final ⚫The general behavior of pressure with speed is true even for gases ⚫As the speed increases, the pressure decreases Applications of Fluid Dynamics