Concept explainers
Consider Problem 6.16 with the diffuser directed upward. Assuming that the flow is uniform at each section, derive and plot the acceleration of a fluid particle for an inlet speed of Vi = 12 m/s. Plot the pressure gradient through the diffuser, and find its maximum value. If the pressure gradient must be no greater than 20 kPa/m, how long would the diffuser have to be?
6.16 A diffuser for an incompressible, inviscid fluid of density ρ = 1000 kg/m3 consists of a horizontal diverging section of pipe. At the inlet the diameter is Di = 0.25 m, and at the outlet the diameter is Do = 0.75 m. The diffuser length is L = 1 m, and the diameter increases linearly with distance x along the diffuser. Derive and plot the acceleration of a fluid particle, assuming uniform flow at each section, if the speed at the inlet is Vi = 5 m/s. Plot the pressure gradient through the diffuser, and find its maximum value. If the pressure gradient must be no greater than 25 kPa/m, how long would the diffuser have to be?
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
INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
DeGarmo's Materials and Processes in Manufacturing
Manufacturing Engineering & Technology
Mechanics of Materials
Thinking Like an Engineer: An Active Learning Approach (4th Edition)
Mechanics of Materials (10th Edition)
- The velocity of an incompressible fluid flowing through a vertically placed pipe of radius RCreate your profile (vz). Note: The end effects will be neglected, the fluid flows in the laminar region.arrow_forwardThe plunger diameter of a single-acting reciprocating pump is 115 mm and the stroke is 230 mm. The suction pipe is 90 mm in diameter and 4.2 m long. If cavitation takes place at the suction head of 4 m, the barometer stands at 10.3 m of water, and the water level in the sump is 3 m below the pump cylinder axis. 3.1 Find the maximum allowable speed to operate the pump 3.2 What power is expected in overcoming friction at this speed, takef = 0.01arrow_forwardWater flows out of 5 mm x 200 mm slots in a sprinkler as shown. The mass flow rate is 15 kg/s. 200 mm 250 mm a. Find the torque required to prevent the sprinkler from rotating. b. Find the rotation rate of the frictionless sprinkler when released.arrow_forward
- An artery reduces in area from 0.00034 m2 at its inlet to 0.00022 m2 at its outlet. Blood enters the artery at velocity 0.15 m/s and pressure 15,000 Pa. Blood leaves the artery at a pressure 10,000 Pa. Assuming that the artery may be modelled as a straight, circular tube and neglecting gravity what is the force exerted on the artery by the fluid. The density of blood is 1050 kg/m3. Give your answer in Newtons.arrow_forward3. A water jet pump has an area Aj = 50 cm² and a jet velocity v = 25 m/s, which entrains a secondary stream of water having a velocity vs = 3 m/s in a pipe of total area 4= 500 cm². At section 2, the water is thoroughly mixed. Assuming one-dimensional flow and neglecting wall shear, estimate the following. a. The average velocity at section 2 b. The change in pressure from plane 1 to 2, (P2-P1), assuming the pressure of the jet and secondary stream to be the same at section 1 0₂arrow_forwardA water jet 50 mm in diameter impinges on a cone as shown in Fig. 4. If the water velocity has the same magnitude at all points in the flow, calculate the thickness of the liquid layer at a location where the cone diameter is 0.5 m. If the mass flowrate of the water is 16 kg/s, calculate the flows peed.arrow_forward
- 4.19 A sharpe-edged orifice has a diameter of 25.4 mm and coefficients of veloc- ity and contraction of 0.98 and 0.62, respectively. If the jet drops 939 mm in a horizontal distance of 2496 mm, determine the flow in m'/s and the head on the orifice.arrow_forward6.36 This two-dimensional water (at 50°F) jet is deflected by the two-dimensional vane, which is moving to the right with a speed of 60 ft/s. The initial jet is 0.30 ft thick (vertical dimension), and its speed is 100 ft/s. What power per foot of the jet (normal to the page) is transmitted to the vane? See §6.5 for useful knowledge about moving CVs.arrow_forward1. A piston-cylinder is producing a viscous oil flow, which has the flow rate of Q, radius R=1.5 mm, and stroke L-5 mm. The fluid density is p = 800 kg/m³ and the viscosity is μ = 0.5 Pa-s. The pressure to drive the flow is p=6.25 Pa. a. How many non-dimensional groupings can be obtained? Derive them. b. If the flow transitions at Re = PV(2R) =2300. Is the generated flow laminar or turbulent given Q=20 mL/s? LL c. Assume the pressure gradient is uniform on the cross-section and can be calculated using OP=-. The velocity profile in the cylinder is u(r) = ax - [1-(²]. Sketch the velocity profile. Calculate the shear stress at the R² ap 2UÔI cylinder wall and label the direction. d. Calculate the flow rate Q with the velocity profile in (c).. e. If the shear stress is uniform over the cross-section, i.e. T = C, what's the pressure gradient distribution and sketch it? L L. Rarrow_forward
- If 475mm diameter pipeline (A) conveying water splits into 2 smaller pipelines (B) and (C), 275mm and 200mm respectively in diameter. If the velocity of flow in (A) is 2.8 m/sec and the flowrate in (B) is twice that in (C), calculate the flowrate in all pipes and the velocity of flow in pipes (B) and (C).arrow_forwardconsider the following conditions: a centrifugal pump has diameters d1 = 7 in, d2 = 13 in, blade widths b1 = 4 in, b2 = 3 in, blade angles β1 = 25° and β2 = 40°, and rotates at 1160 r/min. If the fluid is gasoline at 20°C (ρ = 1.319 slugs/ft^3) and the flow enters the blades radially, estimate the theoretical or “design” quantities. (a) design flow rate in gal/min (b) horsepower (c) head in ftarrow_forward1. A piston-cylinder is producing a viscous oil flow, which has the flow rate of Q, radius R=1.5 mm, and stroke L-5 mm. The fluid density is p = 800 kg/m³ and the viscosity is μ = 0.5 Pa-s. The pressure to drive the flow is p-6.25 Pa. a. How many non-dimensional groupings can be obtained? Derive them. b. If the flow transitions at Re = V(2R) =2300. Is the generated flow laminar or turbulent given Q=20 mL/s? c. Assume the pressure gradient is uniform on the cross-section and can be calculated using - The velocity profile in the cylinder is u(r) = [1-2²]. Sketch the velocity profile. Calculate the shear stress at the ax 2μ δχ cylinder wall and label the direction. d. Calculate the flow rate Q with the velocity profile in (c).. e. If the shear stress is uniform over the cross-section, i.e. T = C, what's the pressure gradient distribution and sketch it? L r L. Rarrow_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