Explanation Given information: The flow is steady, three-dimensional and incompressible. Write the expression for the velocity field. V → = ( a x z 2 − b y ) i → + c x y z j → + ( d z 3 + e x z 2 ) k → ....... (I) Here, unit vector along x direction is i → , unit vector along y direction is j → and unit vector along y direction is k → , constants are a , b , c , d and e and position coordinates are z , y and z . Write the expression for the continuity equation. ∂ u ∂ x + ∂ v ∂ y + ∂ w ∂ z = 0 ...... (II) Here, velocity components are u , v and w in x , y and z -direction. Calculation: Substitute ( a x z 2 − b y ) for u , c x y z for v and ( d z 3 + e x z 2 ) for w in Equation (II). ∂ ( a x z 2 − b y ) ∂ x + ∂ ( c x y z ) ∂ y + ∂ ( d z 3 + e x z 2 ) ∂ z = 0 ∂ ∂ x ( a x z 2 − b y ) + ∂ ∂ y ( c x y z ) + ∂ ∂ z ( d z 3 + e x z 2 ) = 0 a z 2 − 0 + c x z + 3 d z 2 + 2 e x z = 0 a z 2 + c x z + 3 d z 2 + 2 e x z = 0 ...... (III) Equate similar terms in Equation (III). a = − 3 d c = − 2 e ...... (IV) The each component of velocity field in Equation (I) must be dimensionally homogenous and should have dimensions of velocity. Write dimensions of velocity u -component, u = ( a x z 2 − b y ) ( L t ) = ( a ( L 3 ) − b ( L ) )

Fluid Mechanics: Fundamentals and Applications

4th Edition

ISBN: 9781259696534

Author: Yunus A. Cengel Dr., John M. Cimbala

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid stat…

Videos

Question

Chapter 9, Problem 115P

To determine

The conditions for flow to be incompressible.

The primary dimensions of constants.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9, Problem 114P

Chapter 9, Problem 116P

Students have asked these similar questions

The gears shown in the figure have a diametral pitch of 2 teeth per inch and a 20° pressure angle. The pinion rotates at 1800 rev/min clockwise and transmits 200 hp through the idler pair to gear 5 on shaft c. What forces do gears 3 and 4 transmit to the idler shaft? TS I y 18T 32T This a 12 x 18T C 48T 5

Question 1. Draw 3 teeth for the following pinion and gear respectively. The teeth should be drawn near the pressure line so that the teeth from the pinion should mesh those of the gear. Drawing scale (1:1). Either a precise hand drawing or CAD drawing is acceptable. Draw all the trajectories of the involute lines and the circles. Specification: 18tooth pinion and 30tooth gear. Diameter pitch=P=6 teeth /inch. Pressure angle:20°, 1/P for addendum (a) and 1.25/P for dedendum (b). For fillet, c=b-a.

5. The figure shows a gear train. There is no friction at the bearings except for the gear tooth forces. The material of the milled gears is steel having a Brinell hardness of 170. The input shaft speed (n2) is 800 rpm. The face width and the contact angle for all gears are 1 in and 20° respectively. In this gear set, the endurance limit (Se) is 15 kpsi and nd (design factor) is 2. (a) Find the revolution speed of gear 5. (b) Determine whether each gear satisfies the design factor of 2.0 for bending fatigue. (c) Determine whether each gear satisfies the design factor of 2.0 for surface fatigue (contact stress). (d) According to the computation results of the questions (b) and (c), explain the possible failure mechanisms for each gear. N4=28 800rpm N₁=43 N5=34 N₂=14 P(diameteral pitch)=8 for all gears Coupled to 2.5hp motor

Chapter 9 Solutions

Fluid Mechanics: Fundamentals and Applications

Ch. 9 - Explain the fundamental differences between a flow...Ch. 9 - What does it mean when we say that two more...Ch. 9 - The divergence theorem is v.cdv=A c . n dA Ch. 9 - Prob. 4CP Ch. 9 - Prob. 5CP Ch. 9 - Prob. 6CP Ch. 9 - Prob. 7P Ch. 9 - Prob. 8P Ch. 9 - Let vector G=2xzi12x2jz2kk . Calculate the...Ch. 9 - Prob. 10P

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.

The conditions for flow to be incompressible. The primary dimensions of constants.