Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 14, Problem 89P
To determine
The angle through which wickets gates should turn the flow.
The swirl angle
The power output of turbine.
The net required head.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A Francis radial-flow hydroturbine has the following dimensions, where location 2 is the inlet and location 1 is the outlet: r2 = 2.00 m, r1 = 1.30 m, b2 = 0.85 m, and b1 = 2.10 m. The runner blade angles are ?2 = 71.4° and ?1 = 15.3° at the turbine inlet and outlet, respectively. The runner rotates at n. = 160 rpm. The volume flow rate at design conditions is 80.0 m3/s. Irreversible losses are neglected in this preliminary analysis. Calculate the angle ?2 through which the wicket gates should turn the flow, where ?2 is measured from the radial direction at the runner inlet. Calculate the swirl angle ?1, where ?1 is measured from the radial direction at the runner outlet. Does this turbine have forward or reverse swirl? Predict the power output (MW) and required net head (m).
A Francis radial-flow hydro turbine has the following dimensions, where
location 2 is the inlet and location 1 is the outlet: r2 = 2 m, rı = 1.34 m, b2 = 0.8
m, and bi = 2.2 m. The runner blade angles are ß = 82° and Bi = 46° at the
turbine inlet and outlet, respectively (Figure 3.1). The runner rotates at n = 120
rpm. The volume flow rate at design conditions is 300 m³/s. Irreversible losses
are neglected in this preliminary analysis.
i.
Calculate the angle æ wicket gate should turn the flow, where æ is
measured from the radial direction at the runner inlet.
ii.
Calculate the swirl angle, a, where a is measured from the radial
direction at the runner outlet.
iii.
Does this turbine have a forward or reverse swirl?
iv.
Predict the power output (kW) and required net head (m).
The dimensions of a Francis radial-flow hydroturbine are r2 = 2.00 m, r1 = 1.30 m, b2 = 0.85 m, and b1 = 2.10 m, where location 2 is the inlet and location 1 is the outlet. At the turbine inlet and outflow, the runner blade angles are β2 = 71.4° and β1 = 15.3°, respectively. The runner rotates at a rate of ń = 160 rpm. At design conditions, the volume flow rate is 80.0 m3 /s.
(a) State the necessary assumptions and calculate the angle α2 at which the wicket gates should turn the flow (Figure Q1), with α2 measured from the radial direction at the runner inlet.
(b) Calculate the swirl angle α1 (Figure Q1), where α1 is the angle measured from the radial direction at the runner output.
(c) Calculate the needed net head and power output.
(d) Discuss the actual power output and head required for actual case of the turbine (irreversibility not neglected).
(Properties For water at 20oC, ρ = 998.0 kg/m3)
Chapter 14 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 14 - What is the more common term for an...Ch. 14 - What the primary differences between fans,...Ch. 14 - List at least two common examples of fans, of...Ch. 14 - Discuss the primary difference between a porn...Ch. 14 - Explain why there is an “extra” term in the...Ch. 14 - For a turbine, discuss the difference between...Ch. 14 - Prob. 7CPCh. 14 - Prob. 8PCh. 14 - Prob. 9PCh. 14 - Prob. 10CP
Ch. 14 - There are three main categories of dynamic pumps....Ch. 14 - For each statement about cow cetrifugal the...Ch. 14 - Prob. 13CPCh. 14 - Consider flow through a water pump. For each...Ch. 14 - Write the equation that defines actual (available)...Ch. 14 - Consider a typical centrifugal liquid pump. For...Ch. 14 - Prob. 17CPCh. 14 - Consider steady, incompressible flow through two...Ch. 14 - Prob. 19CPCh. 14 - Prob. 20PCh. 14 - Suppose the pump of Fig. P1 4-19C is situated...Ch. 14 - Prob. 22PCh. 14 - Prob. 23EPCh. 14 - Consider the flow system sketched in Fig. PI 4-24....Ch. 14 - Prob. 25PCh. 14 - Repeat Prob. 14-25, but with a rough pipe-pipe...Ch. 14 - Consider the piping system of Fig. P14—24. with...Ch. 14 - The performance data for a centrifugal water pump...Ch. 14 - For the centrifugal water pump of Prob. 14-29,...Ch. 14 - Suppose the pump of Probs. 14-29 and 14-30 is used...Ch. 14 - Suppose you are looking into purchasing a water...Ch. 14 - The performance data of a water pump follow the...Ch. 14 - For the application at hand, the flow rate of...Ch. 14 - A water pump is used to pump water from one large...Ch. 14 - For the pump and piping system of Prob. 14-35E,...Ch. 14 - A water pump is used to pump water from one large...Ch. 14 - Suppose that the free surface of the inlet...Ch. 14 - Calculate the volume flow rate between the...Ch. 14 - Comparing the results of Probs. 14-39 and 14-43,...Ch. 14 - Prob. 45PCh. 14 - The performance data for a centrifugal water pump...Ch. 14 - Transform each column of the pump performance data...Ch. 14 - 14-51 A local ventilation system (a hood and duct...Ch. 14 - Prob. 52PCh. 14 - Repeat Prob. 14-51, ignoring all minor losses. How...Ch. 14 - Suppose the one- way of Fig. P14-51 malfunctions...Ch. 14 - A local ventilation system (a hood and duct...Ch. 14 - For the duct system and fan of Prob. 14-55E,...Ch. 14 - Repeat Prob. 14-55E, ignoring all minor losses....Ch. 14 - A self-priming centrifugal pump is used to pump...Ch. 14 - Repeat Prob. 14-60. but at a water temperature of...Ch. 14 - Repeat Prob. 14-60, but with the pipe diameter...Ch. 14 - Prob. 63EPCh. 14 - Prob. 64EPCh. 14 - Prob. 66PCh. 14 - Prob. 67PCh. 14 - Prob. 68PCh. 14 - Prob. 69PCh. 14 - Two water pumps are arranged in Series. The...Ch. 14 - The same two water pumps of Prob. 14-70 are...Ch. 14 - Prob. 72CPCh. 14 - Name and briefly describe the differences between...Ch. 14 - Discuss the meaning of reverse swirl in reaction...Ch. 14 - Prob. 75CPCh. 14 - Prob. 76CPCh. 14 - Prob. 77PCh. 14 - Prob. 78PCh. 14 - Prob. 79PCh. 14 - Prob. 80PCh. 14 - Wind ( =1.204kg/m3 ) blows through a HAWT wind...Ch. 14 - Prob. 82PCh. 14 - Prob. 84CPCh. 14 - A Francis radial-flow hydroturbine has the...Ch. 14 - Prob. 87PCh. 14 - Prob. 88PCh. 14 - Prob. 89PCh. 14 - Prob. 90CPCh. 14 - Prob. 91CPCh. 14 - Discuss which dimensionless pump performance...Ch. 14 - Prob. 93CPCh. 14 - Prob. 94PCh. 14 - Prob. 95PCh. 14 - Prob. 96PCh. 14 - Prob. 97PCh. 14 - Prob. 98PCh. 14 - Prob. 99PCh. 14 - Prob. 100EPCh. 14 - Prob. 101PCh. 14 - Calculate the pump specific speed of the pump of...Ch. 14 - Prob. 103PCh. 14 - Prob. 104PCh. 14 - Prob. 105PCh. 14 - Prob. 106PCh. 14 - Prob. 107EPCh. 14 - Prob. 108PCh. 14 - Prob. 109PCh. 14 - Prob. 110PCh. 14 - Prove that the model turbine (Prob. 14-109) and...Ch. 14 - Prob. 112PCh. 14 - Prob. 113PCh. 14 - Prob. 114PCh. 14 - Prob. 115CPCh. 14 - Prob. 116CPCh. 14 - Prob. 117CPCh. 14 - Prob. 118PCh. 14 - For two dynamically similar pumps, manipulate the...Ch. 14 - Prob. 120PCh. 14 - Prob. 121PCh. 14 - Prob. 122PCh. 14 - Calculate and compare the turbine specific speed...Ch. 14 - Prob. 124PCh. 14 - Prob. 125PCh. 14 - Prob. 126PCh. 14 - Prob. 127PCh. 14 - Prob. 128PCh. 14 - Prob. 129PCh. 14 - Prob. 130PCh. 14 - Prob. 131PCh. 14 - Prob. 132PCh. 14 - Prob. 133PCh. 14 - Prob. 134PCh. 14 - Prob. 135PCh. 14 - A two-lobe rotary positive-displacement pump moves...Ch. 14 - Prob. 137PCh. 14 - Prob. 138PCh. 14 - Prob. 139PCh. 14 - Prob. 140PCh. 14 - Which choice is correct for the comparison of the...Ch. 14 - Prob. 142PCh. 14 - In a hydroelectric power plant, water flows...Ch. 14 - Prob. 144PCh. 14 - Prob. 145PCh. 14 - Prob. 146PCh. 14 - Prob. 147PCh. 14 - Prob. 148PCh. 14 - Prob. 149PCh. 14 - Prob. 150PCh. 14 - Prob. 151P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Q1): Impulse turbine diameter = 3.2m O1 = O2 Angular velocity = 25 rad/s Absolute velocities V1 = 140m/s and V2 = 110m/s Power developed by the wheel = 300kw Calculate: Jet 25mmd VI V: 1. the blade velocity. 2. the force exerted and 3. the angle O.arrow_forward4. A centrifugal pump delivers water to a height of 22 metres at a speed of 800 r.p.m. The velocity of flow is constant at a speed of 2-0 m/s and the outlet vane anglc is 45°. If the pump discharges 225 litres of water per second, find the diameter of the impeller and width of the impcller at oudet. (Ans. 375 mm: 95 mm)arrow_forwardA centrifugal pump with a 3-inches diameter impeller rotating at 1150 rpm delivered 400 gpm of water 80ºF at 250 ft total head. Find the impeller diameter of a geometrically similar pump rotating at 1750 rpm delivering 500 gpm. What is the total head of the second pump.arrow_forward
- A 15 in. diameter fan operates at 1600 rpm and develops a head of 6 in. of water anddelivers 120 cfm. What volumetric capacity for geometrically similar fan will develop 6 in ofwater at 1300 rpm?arrow_forwardA pump draws water from open reservoir A at 20 ft above pump centerline and lifts to an open reservoir B at 280 ft above pump centerline. The loss of head at the suction is 3 times the velocity head at the 6 inches suction pipe and at the discharge is 20 times the velocity head at the 4 inches discharge pipe. The pump discharge is 200 GPM. a. The total dynamic head in ft. b. The water power in horsepowerarrow_forwardPumps: A centrifugal pump having 4 stages in parallel, delivers 18 kiloliters/min of liquid against a head of 25 m. The diameter of the impellers being 24 cm and the speed of 1800 rpm. A pump is to be made up with a number of stages in series of similar construction to that of the first pump to run at 1250 rpm and to deliver 15 kiloliters/min against a totalhead of 250 m. Find the diameter of the impellers and the number of stages required in this case. Answer: D = 46.63 cm, n = 6 stagesarrow_forward
- PROBLEM 1 In an axial flow pump, the rotor has an outer diameter of 75 om and an inner diameter of 40 cm, it rotates at 500 rpm. At the mean blade radius, the inlet blade angle is 12 deg and the outlet blade angle is 15 deg Sketch the corresponding velocity diagrams at inlet and outlet and estimate the following (1) the head the pump will generate, A. 11.2 m B 17 6m C5.4 m D 19 8 m (ii) the discharge or rate of flow in l/s B. 203 s C.407 Us D 609 Vs A 705 Vs (iii) the shaft h.p input required to drive the pump and B 230 hp C:300 hp D 401 hp A 170 hp (V) the specific speed of the pump. B. 65 C.45 D 75 A 80arrow_forwardUsing the performance curve of pump A given in Example VIc.3.2 (41.5” and 710 rpm) and find: a) total dynamic head of a similar pump (pump B), at peak efficiency, having a diameter of 35 inches. Assume that both pumps A and B are operating at the same speed. b) pump head if pump B is now operating at 1170 rpm. [Ans.: a) H = 192 ft and b) H = 521.5 ft].arrow_forwardThe dimensions of a Francis radial-flow hydroturbine are r2 = 2.00 m, r1 = 1.30 m, b2 = 0.85 m, and b1 = 2.10 m, where location 2 is the inlet and location 1 is the outlet. At the turbine inlet and outflow, the runner blade angles are β2 = 71.4° and β1 = 15.3°, respectively. The runner rotates at a rate of ń = 160 rpm. At design conditions, the volume flow rate is 80.0 m3 /sarrow_forward
- An inflow to a turbine with a discharge of 20 m³/s leads to a ration speed of 150 rpm. The blades inlet edges have an angle of 120° to the direction of whirl. The outer diameter of the runner is 1.5 m and the runner inlet width is 1.0 m. 5. (a) To plot the velocity triangle at the blade outlet edge. (b) Assume design operating conditions and no velocity of whirl at outlet, calculate the power delivered by the runner. (c) The elevation difference between the head race and the tail race is 23 m and the head available to the turbine is 20 m, what is the hydraulic efficiency of the turbine and overall efficiency? (d) If a model of 1/10 full scale is constructed to operate under a head of 10 m, what must be its speed, power, water consumption and overall efficiency to run under the similar conditions to the prototype?arrow_forwardFigure below shows the performance curve family of Model 5009 Centrifugal pumps of Taco Pump Inc., running at a fixed speed of N = 1160 rpm. For the pump with the impeller diameter D = 8.625 in., you are asked to determine the best efficiency point (BEP) of the given pump. What is the pump efficiency at BEP? HEAD IN FEET 50 0 0 0 0 40 20 10 O 81% 8.625" 30 (219mm). O 51% O 71% ○ 61% O Taco L/SEC 5 9.25" (235mm) 8.00" (203mm) 7.375" (187mm) 6.75" (171mm) 0 10 15 125 Model 5009 FI & CI Series 20 25 CURVES BASED ON CLEAR WATER WITH SPECIFIC GRAVITY OF 1.0 8 8 52 75% 77% 30 79% 1160 RPM FEBRUARY 19. 2002 35 40 45 REQUIRED NPSH olº 1.5HP (1.1KW) dot 17% Curve no. 2140 Min. Imp. Dia. 6.75" Size 6 x 5 x 9.0 50 55 60 75% 72% 250 375 500 625 FLOW IN GALLONS PER MINUTE 8% 2HP(1.5KW) 750 %09. 55% (2.2KW) 3HP 7.5HP(5.6KW) 2015 do 35% 875 FEET 15 12 -9 6 SHP(3.7KW) 3 0 10 8 NPSH 1000 HEAD IN METERS 5 KPo 45 -36 27 18 9 -0 100 -80 60 -40 2 -20 8 HEAD IN KILOPASCALSarrow_forwardIn a certain hydraulic turbomachine, the following data apply:Inlet blade velocity is 20 m/s. Vu1=21 m/s; Vr1=10 m/s.At the exit, V2 is purely axial and has a value of 14 m/s, and blade speed is9 m/s. Is this power absorbing or power producing? Find E and the changes instatic and stagnation pressures. Would this machine be classified as a purelyradial, purely axial, or mixed flow type?Ans: E=420 J/kg; Δpstag=420 kPa; Δpstat=247.4 kPaarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- 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
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Fluid Mechanics - Viscosity and Shear Strain Rate in 9 Minutes!; Author: Less Boring Lectures;https://www.youtube.com/watch?v=_0aaRDAdPTY;License: Standard youtube license