An incompressible liquid with negligible viscosity and density ρ = 1.75 slug/ft3 flows steadily through a horizontal pipe. The pipe cross-section area linearly varies from 15 in.2 to 2.5 in.2 over a length of 10 feet. Develop an expression for and plot the pressure gradient and pressure versus position along the pipe, if the inlet centreline velocity is 5 ft/s and inlet pressure is 35 psi. What is the exit pressure? Hint: Use relation
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Additional Engineering Textbook Solutions
Engineering Mechanics: Dynamics (14th Edition)
Introduction To Finite Element Analysis And Design
Thinking Like an Engineer: An Active Learning Approach (3rd Edition)
Degarmo's Materials And Processes In Manufacturing
Engineering Mechanics: Statics
Engineering Mechanics: Statics
- Liquid is pushed through the narrow gap formed between two glass plates. Thedistance between the plates is h and the width of the plate is b . Assuming that theflow is laminar, two-dimensional and fully developed, derive a formula for thelongitudinal pressure gradient in terms of the volumetric flow rate, Q, the fluid viscosityand the distances b and h .In an example the above conditions apply with b = 0.10 m and h = 0.00076 m. Theliquid is glycerine that has an absolute viscosity of 0.96 N s/m². A pressure differenceof 192 kN/m² is applied over a distance of 0.24 m. Calculate the maximum velocity thatoccurs in the centre plane of the gap and the mean velocity.Answer 0.06 m/sarrow_forwardThe Reynolds number, pVD/μ is a very important parameter in fluid mechanics. Determine its value for ethyl alcohol flowing at a velocity of 2 m/s through a 2-in.- diameter pipe. Re=arrow_forwardYour team is designing a chemical processing plant. You are the liquid handling and transportation specialist, and you need to transport a solvent (μ = 3.1 cP, ρ = 122k kg/m3) from a storage tank to a reaction vessel. Due to other equipment constraints, the fluid velocity must be 0.8 m/sec, and you must use stainless steel piping (ε = 0.00015 mm) with a total length (L) of 12 m. Determine the pipe inner diameter (ID) you will need to achieve a pressure drop of 0.3 kPa. Use the Moody chart.arrow_forward
- Ethyl alcohol flows in the pipe as shown in Figure below of specific weight 19 lb/ft^ 3 . What is the mass flow rate? If viscous effects are neglectedTake the specific weight for mercury equal to 846 and for water equal to 62.4 at 68 Farrow_forwardQ: Consider fully developed laminar flow in the annular space formed by the two concentric cylinders shown in the below diagram. The outer pipe is stationary, and the inner pipe moves in the x direction with speed V For pressure gradient, , and the inner cylinder stationary, let ro = R and r = kR, The velocity profile is ax given by: др + 4μ. θα Find: 1- Volume flow rate (Q). 2- An expression for the average velocity (V) 3- Fork → 0, find Q and V 6arrow_forwardGiven an open tank filled with oil that is discharging through a 35-meter long commercial annulus pipe as shown in figure below. Calculate the volume flowrate at point 2 when the oil surface is 5 meters from it. Neglect entrance effects take kinematic viscosity equal to 4 x10* m/s. (Ro and Ri are radaii). h = 5 m Ro = 5 cm %D Ri = 2 cm Q. V L= 35 m Oil (SG = 0.9) %3Darrow_forward
- The ethanol solution is pumped into a vessel 25 m above the reference point through a 25 mm diameter steel pipe at a rate of 8 m3 / hr. The pipe length is 40 m and there are 2 elbows. Calculate the power requirements of the pump. The properties of the solution are density 975 kg / m3 and viscosity 4x 10-4 Pa s. a. Reynold number = Answer. b. Loss of Energy along the straight pipe = Answer J / kg. c. Energy Loss at curves = Answer J / kg. d. Total energy to overcome friction = Answer J / kg. e. Energy to increase water according to height = Answer J / kg. f. The theoretical energy requirement for the pump is kg ethanol / second = Answer J / kg. g. Actual pump power requirement = Answer watt.arrow_forwardThe ethanol solution is pumped into a vessel 25 m above the reference point through a 25 mm diameter steel pipe at a rate of 8 m3 / hr. The pipe length is 40 m and there are 2 elbows. Calculate the power requirements of the pump. The properties of the solution are density 975 kg / m3 and viscosity 4x 10-4 Pa s. a. Reynold number = Answer. b. Loss of Energy along the straight pipe = AnswerJ / kg. c. Losing Energy at curves = AnswerJ / kg. d. Total energy to overcome friction = AnswerJ / kg. e. Energy to increase water according to height = AnswerJ / kg. f. The theoretical energy requirement of the pump ethanol / second = AnswerJ / kg. g. Actual pump power requirement = Answerwatt.arrow_forward3. Explain briefly what is meant by fully developed laminar flow. The velocity u at any radius r in fully developed laminar flow through a straight horizontal pipe of internal radius ro is given by u= (1/4µ)(ro2-r2)dp/dx dp/dx is the pressure gradient in the direction of flow and u is the dynamic viscosity. Show that the pressure drop over a length L is given by the following formula. Ap=32μLu/D² The wall skin friction coefficient is defined as C = 21/(pum²). Show that C= 16/Re where Re = pumD/μ and p is the density, um is the mean velocity and to is the wall shear stress.arrow_forward
- FLUID FLOW Example 5: A liquid food with a density of 800 kg/m³ is being transported at a rate of 5 ton/h through the system shown below. If the pressure at point 1 is 20 kPa gage, determine the pressure at point 2. Neglect friction losses. Example 5 P₁ = 20 kPa D₁ = 0.08 m 6 m 2 FLUID FLOW P₂ = ? D₂ = 0.025 marrow_forwardThe ethanol solution is pumped into a vessel 25 m above the reference point through a 25 mm diameter steel pipe at a rate of 8 m3/hour. The length of the pipe is 35m and there are 2 elbows. Calculate the pump power requirement. The properties of the solution are density 975 kg/m3 and viscosity 4x 10-4 Pa s. a. Reynolds number = b. Energy Loss along a straight pipe = J/kg. c. Energy Loss in turns = J/kg. d. Total energy to overcome friction = J/kg. e. Energy to raise water to height = J/kg. f. Theoretical energy requirement of the pump kg ethanol/second = J/kg. g. Actual pump power requirement = watt.arrow_forwardQ1\ A crude oil of viscosity 0.85 poise and relative density 0.7 is flowing through a horizontal circular pipe of diameter 126 mm and of length 12 m. Calculate the difference of pressure at the two ends of the pipe, if 125 kg of the oil is collected in a tank in 40 seconds.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY