Introduction to Fluid Mechanics Chapter 8 Internal Incompressible

Introduction to Fluid Mechanics Chapter 8 Internal Incompressible Viscous Flow © Pritchard

Main Topics Entrance Region Fully Developed Laminar Flow Between Infinite Parallel Plates Fully Developed Laminar Flow in a Pipe Turbulent Velocity Profiles in Fully Developed Pipe Flow Energy Considerations in Pipe Flow Calculation of Head Loss Solution of Pipe Flow Problems Flow Measurement © Pritchard

Entrance Region © Pritchard

Daerah berkembangnya profil kecepatan dari linier di hulu menjadi parabolik disebut entrance region, sedangkan daerah dengan profik kecepatan berbentuk parabolik disebut fully developed region.

Fully Developed Laminar Flow Between Infinite Parallel Plates Both Plates Stationary © Pritchard

Problems 8. 1 Standar air enters a 150 mm diameter duct. Find the volume flow rate at which the flow becomes turbulent. At this flow rate, estimate the entrance length required to establish fully developed flow

Fully Developed Laminar Flow Between Infinite Parallel Plates Both Plates Stationary • Transformation of Coordinates © Pritchard

Fully Developed Laminar Flow Between Infinite Parallel Plates Both Plates Stationary • Shear Stress Distribution • Volume Flow Rate © Pritchard

Fully Developed Laminar Flow Between Infinite Parallel Plates Both Plates Stationary • Flow Rate as a Function of Pressure Drop • Average and Maximum Velocities © Pritchard

Fully Developed Laminar Flow Between Infinite Parallel Plates Upper Plate Moving with Constant Speed, U © Pritchard

Problems 8. 9 Viscous oil flow steadily between parallel plates. The flow is fully developed and laminar. The pressure gradient is 1, 25 k. Pa/m and the channel half-width is h = 1, 5 mm. Calculate the magnitude and direction of the wall shear stress at the upper plate surface. Find the volume flow rate through the channel (μ = 0, 50 Ns/m²)

Problems 8. 23 Two immiscible fluids are contained between infinite parallel plates. The plates are separated by distance 2 h, and the two fluid layers are of equal thickness h; the dynamic viscosity of the upper fluid is three times that of the lower fluid. If the lower plate is stationary and the upper plate moves at constant speed U = 6, 1 m/s, what is the velocity at the interface? Assume laminar flows, and that the pressure gradient in the direction of flow is zero.

Fully Developed Laminar Flow in a Pipe Velocity Distribution Shear Stress Distribution © Pritchard

Fully Developed Laminar Flow in a Pipe Volume Flow Rate as a Function of Pressure Drop © Pritchard

Fully Developed Laminar Flow in a Pipe Average Velocity Maximum Velocity © Pritchard

Turbulent Velocity Profiles in Fully Developed Pipe Flow © Pritchard

Turbulent Velocity Profiles in Fully Developed Pipe Flow © Pritchard

Problems 8. 47 A hypodermic needle, with inside diameter d = 0, 127 mm and length L = 25 mm, is used to inject saline solution with viscosity five times that of water. The plunger diameter is D = 10 mm; the maximum force that can be exerted by a thumb on the plunger is F = 33, 4 N. Estimate the volume flow rate of saline that can be produced.

Calculation of Head Loss Major Losses: Friction Factor © Pritchard

Calculation of Head Loss Laminar Friction Factor Turbulent Friction Factor © Pritchard

Calculation of Head Loss © Pritchard

Calculation of Head Loss Minor Losses • Examples: Inlets and Exits; Enlargements and Contractions; Pipe Bends; Valves and Fittings © Pritchard

Calculation of Head Loss Minor Loss: Loss Coefficient, K Minor Loss: Equivalent Length, Le © Pritchard

Calculation of Head Loss Pumps, Fans, and Blowers © Pritchard

Calculation of Head Loss Noncircular Ducts Example: Rectangular Duct © Pritchard

Solution of Pipe Flow Problems Energy Equation © Pritchard

Solution of Pipe Flow Problems Major Losses © Pritchard

Solution of Pipe Flow Problems Minor Losses © Pritchard

Problems 8. 73 Water flows from a horizontal tube into a large tank. The tube is located 2. 5 m below the free surface of water in the tank. The head loss is 2 J/kg. Compute the average flow speed in the tube.

Problems 8. 84 Water flows through a 25 mm diameter tube that suddenly enlarges to a diameter of 50 mm. the flow rate through the enlargement is 1, 25 Liter/s. Calculate the pressure rise across the enlargement. Compare with the value for frictionless flow.

Flow Measurement Direct Methods • Examples: Accumulation in a Container; Positive Displacement Flow meter Restriction Flow Meters for Internal Flows • Examples: Orifice Plate; Flow Nozzle; Venturi; Laminar Flow Element © Pritchard

Flow Measurement Linear Flow Meters • Examples: Float Meter (Rotameter); Turbine; Vortex; Electromagnetic; Magnetic; Ultrasonic © Pritchard

Flow Measurement Traversing Methods • Examples: Pitot (or Pitot Static) Tube; Laser Doppler Anemometer © Pritchard

Problems 8. 173 A venture meter with a 762 mm diameter throat is place in a 152 mm diameter line carrying water at 24˚C. The pressure drop between the upstream tap and the venture throat is 305 mm of mercury. Compute the rate of flow.