Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 6, Problem 50CP
To determine
The angular momentum equation in scalar form about a specified axis of rotation for fixed control volume for steady and uniform flow.
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kindly help me with this problem on momentum transfer
INSTRUCTIONS: Solve the problem neatly and systematically. Use free-floating decimals in all your calculations and in expressing youranswers. Thank you
Choose from the list below the correct equations that correspond to the balance of linear momentum (BoLM) and the balance of angular momentum (BOAM) for
an incompressible hyperelastic material with stored energy function W.
BOLM: Poö = V · (DW(F) – pJF-T) + pofm
BOAM: always satisfied
None of the above
BOLM: Poö = V · (DW (F) – pJF-")+ pofm
BOAM: SR = SR
BOLM: Poë = V · DW (F)+ pofm
BOAM: always satisfied
(E) A uniform stream of fluid with speed U at infinity flows two-dimensionally and irrota-
tionally towards a circular cylinder of radius a. The surface of the cylinder is porous and fluid
is drawn inwards with normal velocity 2U inwards at the surface. The circulation about the
cylinder is zero.
1. Find a real velocity potential for the flow.
2. Find a complex velocity potential for the flow.
3. Find any stagnation points in the flow
4. Find a streamfunction for the flow.
5. Sketch the streamlines of the flow, distinguishing quantitatively between the fluid entering
the cylinder and the fluid passing the cylinder.
Chapter 6 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 6 - Express Newton’s second law of motion for rotating...Ch. 6 - Express Newton’s first, second, and third laws.Ch. 6 - Is momentum a vector? If so, in what direction...Ch. 6 - Express the conservation of momentum principle....Ch. 6 - How do surface forces arise in the momentum...Ch. 6 - Explain the importance of the Reynolds transport...Ch. 6 - What is the importance of the momentum-flux...Ch. 6 - Write the momentum equation for steady...Ch. 6 - In the application of the momentum equation,...Ch. 6 - Two firefighters are fighting a fire with...
Ch. 6 - A rocket in space (no friction or resistance to...Ch. 6 - Describe in terms of momentum and airflow how a...Ch. 6 - Does it take more, equal, or less power for a...Ch. 6 - In a given location, would a helicopter require...Ch. 6 - Describe body forces and surface forces, and...Ch. 6 - A constant-velocity horizontal water jet from a...Ch. 6 - A horizontal water jet of constant velocity V from...Ch. 6 - A horizontal water jet from a nozzle of constant...Ch. 6 - A 2.5-cm-diameter horizontal water jet with a...Ch. 6 - A 90 elbow in a horizontal pipe is used to direct...Ch. 6 - Repeat Prob. 6-20 for the case of another...Ch. 6 - A horizontal water jet impinges against a vertical...Ch. 6 - Water enters a 7-cm-diameter pipe steadily with a...Ch. 6 - A reducing elbow in a horizontal pipe is used to...Ch. 6 - Repeat Prob. 6-24 for the case of = 125°.Ch. 6 - A 100-ft3/s water jet is moving in the positive...Ch. 6 - Reconsider Prob. 6-26E. Using appropriate...Ch. 6 - Commercially available large wind turbines have...Ch. 6 - A fan with 24-in-diameter blades moves 2000 cfm...Ch. 6 - A 3-in-diameter horizontal jet of water, with...Ch. 6 - Firefighters are holding a nozzle at the end of a...Ch. 6 - A 5-cm-diameter horizontal jet of water with a...Ch. 6 - Prob. 33PCh. 6 - A 3-in-diameter horizontal water jet having a...Ch. 6 - An unloaded helicopter of mass 12,000 kg hovers at...Ch. 6 - Prob. 36PCh. 6 - Water is flowing through a 10-cm-diameter water...Ch. 6 - Water flowing in a horizontal 25-cm-diameter pipe...Ch. 6 - Prob. 39PCh. 6 - Water enters a centrifugal pump axially at...Ch. 6 - An incompressible fluid of density and viscosity ...Ch. 6 - Consider the curved duct of Prob. 6-41, except...Ch. 6 - As a follow-up to Prob. 6-41, it turns out that...Ch. 6 - Prob. 44PCh. 6 - The weight of a water tank open to the atmosphere...Ch. 6 - A sluice gate, which controls flow rate in a...Ch. 6 - A room is to be ventilated using a centrifugal...Ch. 6 - How is the angular momentum equation obtained from...Ch. 6 - Prob. 49CPCh. 6 - Prob. 50CPCh. 6 - Prob. 51CPCh. 6 - A large lawn sprinkler with two identical arms is...Ch. 6 - Prob. 53EPCh. 6 - The impeller of a centrifugal pump has inner and...Ch. 6 - Water is flowing through a 15-cm-diameter pipe...Ch. 6 - Prob. 56PCh. 6 - Repeat Prob. 6-56 for a water flow rate of 60 L/s.Ch. 6 - Prob. 58PCh. 6 - Water enters the impeller of a centrifugal pump...Ch. 6 - A lawn sprinkler with three identical antis is...Ch. 6 - Prob. 62PCh. 6 - The impeller of a centrifugal blower has a radius...Ch. 6 - An 8-cm-diameter horizontal water jet having a...Ch. 6 - Water flowing steadily at a rate of 0.16 m3/s is...Ch. 6 - Repeat Prob. 6-66 by taking into consideration the...Ch. 6 - A 16-cm diameter horizontal water jet with a speed...Ch. 6 - Water enters vertically and steadily at a rate of...Ch. 6 - Repeal Prob. 6-69 for the case of unequal anus-the...Ch. 6 - Prob. 71PCh. 6 - Prob. 72PCh. 6 - A spacecraft cruising in space at a constant...Ch. 6 - A 60-kg ice skater is standing on ice with ice...Ch. 6 - A 5-cm-diameter horizontal jet of water, with...Ch. 6 - Water is flowing into and discharging from a pipe...Ch. 6 - Indiana Jones needs So ascend a 10-m-high...Ch. 6 - Prob. 79EPCh. 6 - A walnut with a mass of 50 g requires a force of...Ch. 6 - Prob. 81PCh. 6 - Prob. 82PCh. 6 - A horizontal water jet of constant velocity V...Ch. 6 - Show that the force exerted by a liquid jet on a...Ch. 6 - Prob. 85PCh. 6 - Prob. 86PCh. 6 - Water enters a mixed flow pump axially at a rate...Ch. 6 - Prob. 88PCh. 6 - Water enters a two-armed lawn sprinkler along the...Ch. 6 - Prob. 91PCh. 6 - Prob. 92PCh. 6 - Prob. 93PCh. 6 - Prob. 94PCh. 6 - A water jet strikes a moving plate at velocity...Ch. 6 - Water flows at mass flow rate m through a 90°...Ch. 6 - Prob. 97PCh. 6 - Water shoots out of a Iar2e tank sitting a cart...Ch. 6 - Prob. 99PCh. 6 - Prob. 100PCh. 6 - Prob. 101PCh. 6 - Consider water flow through a horizontal, short...Ch. 6 - Consider water flow through a horizontal. short...Ch. 6 - Prob. 104PCh. 6 - Prob. 105PCh. 6 - Prob. 106PCh. 6 - The velocity of wind at a wind turbine is measured...Ch. 6 - The ve1ocity of wind at a wind turbine is measured...Ch. 6 - Prob. 109PCh. 6 - Prob. 110PCh. 6 - Prob. 111PCh. 6 - Consider the impeller of a centrifugal pump with a...Ch. 6 - Prob. 113PCh. 6 - Prob. 114P
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- Sketch the appropriate diagram and derive the Von-Karman momentum equation. Explain the concept of this equation.arrow_forwardlower end of a string and is moving in a horizontal circle of radius R = 0.15 m at constant speed v = 0.51 m/s. The string has length l and negligible mass and makes an angle 0 with the vertical. The angle 0 is %3D marrow_forwardA reducing elbow in a horizontal pipe is used todeflect water flow by an angle ϴ = 450from the flowdirection while accelerating it (Fig. 3). The elbowdischarges water into the atmosphere at a rate of 30kg/s. The cross-sectional area of the elbow is 150cm2 at the inlet and 25 cm2 at the exit. The elevationdifference between the centers of the exit and theinlet is 40 cm. The mass of the elbow and the waterin it is 50 kg. Determine the anchoring force neededto hold the elbow in place. Take the momentum-fluxcorrection factor to be 1.03 at both the inlet andoutlet. Density of water ρ = 1000 kg/m3, atmosphericpressure 101.0 kPa and g = 9.81 m/s2. Assumesteady, incompressible, frictionless and irrotationalflow.arrow_forward
- Example (1-1): Find the force exerted by a 5 cm diameter water jet directed against a flat plate held normal to the exit of stream. The velocity of the jet is 35 m/s. Example (1-2): A 2.5 cm diameter water jet exerts a force of 90 kN in the direction of flow on a flat plate which is held inclined at an angle of 30° with the axis of stream. Find the rate of flow.arrow_forwardA jet of water strikes a splitter and splits into two streams of equal velocity but unequal thickness. All jets have a width w (into the paper). Friction forces of the water stream on the splitter are negligible. Ignore the weight of the splitter. a) Use the integral mass conservation equation to find an equation for the thickness t of angled exit stream, t = f (h, a) b) Apply the momentum equation in the vertical direction to find an equation 0 = f(a).Hint: the net vertical force on the splitter is zero c) Find an equation Fx = f(p, V, w,h,a,0) for the horizontal force on the splitterarrow_forwardWhat is momentum equation? Describe the properties of Newtonian fluid.arrow_forward
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