Discuss Newton's second law (the linear momentum rela- tion) in these three forms: Σr-mΣr- (mV) na dt Er -_Vpav) Vpdv) 'system Are they all equally valid? Are they equivalent? Are some forms better for fluid mechanics as opposed to solid mechanics?

Discuss Newton's second law (the linear momentum rela- tion) in these three forms: Σr-mΣr- (mV) na dt Er -_Vpav) Vpdv) 'system Are they all equally valid? Are they equivalent? Are some forms better for fluid mechanics as opposed to solid mechanics?

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.9P: When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the...

See similar textbooks

Related questions

Q: You bought a box of orange juice, let’s say 0.5 L, and you want to serve it into cups. But you…

A: In this problem, we will discuss the basic principle of fluid mechanics and projectile motion. The…

Q: Write out the components of the Euler equation as far as possible in Cartesian coordinates (x, y, z)…

A: The vector form of Euler equation is written as:

Q: Given the speed field = ax, – bx, v2 = bx, – ax, v, =crj +x} V3 where a,b and c are constants Check…

Q: The velocity field of incompressible flow in a Cartesian system is represented by V = 2 (2? – y?) î…

A: Given data: V→=2x2-y2i+vj+3k Need to determine the valid expression for "v".

Q: The Stokes-Oseen formula for drag force Fon a sphere of diameter Din a fluid stream of low velocity…

A: As per given question we have determine is this formula dimensionally homogeneous??

Q: Consider a sphere of radius R immersed in a uniform stream Uo, as shown in Fig. P4.7. According to…

A: The given velocity function is The acceleration of the fluid can be calculated as,

Q: Imagine a steady, two-dimensional, incompressible flow that is purely circular in the xy- or…

A: Write the expression of the continuity equation in 2-D polar co-ordinates. Since the flow is…

Q: Using primary dimensions, verify that the Rayleigh number is indeed dimensionless. What other…

A: The Rayleigh number is defined as:

Q: Algebraic equations such as Bernoulli's relation, are dimensionally consistent, but what about…

A: For an equation to be dimensionally consistent, each of the individual components of the equation…

Q: 2. Why the boundary condition of the airfoil surface (here ,we do an assumption, that th airfoil…

A: Most foil shapes require a positive point of attack to produce lift, but cambered airfoils can…

Q: A steady, incompressible, two-dimensional velocity field is given by V-›= (u, ? ) =…

A: Vorticity is mathematically defined as the curl of the velocity field and is hence a measure of…

Q: FLUID MECHANICS 1. Explain and cite an example of the following: a) Fluid Statics b) Fluid…

A: Fluid Statics:- Fluid statics is the part of fluid mechanics that deals with fluids when there is…

Q: When fluid in a pipe is accelerated linearly from rest, itbegins as laminar flow and then undergoes…

Q: The Stokes-Oseen formula for drag force F on a sphere of diameter D in a fluid stream of low…

A: Given data F = 3πμDV +9π16ρV2D2

Q: Liquid flows out of a hole in the bottom of a tank as in FinConsider the case in which the hole is…

A: Given, h2 = 2h1 For a free flowV=2ghV2=2ghsquare of velocity is proportional to…

Q: Incompressible steady fl ow in the inlet between parallelplates in Fig. P3.17 is uniform, u = U 0 =…

A: Take a control volume for the flow as shown in the figure below. Understand that for steady flow.

Q: A steady, incompressible, two-dimensional velocity field is given by V-›= (u, ? ) = (2.5…

Q: Consider the general form of the Reynolds transport theorem (RTT) given by dBsys / dt = d/dt ∫CV ρb…

A: According to the Reynolds transport theorem the linear momentum stored in the control volume is plus…

Q: A steady, two-dimensional, incompressible velocity field has Cartesian velocity components u =…

A: Write the given data: Understand the linear coordinates can be converted into polar coordinates as…

Q: (d) Consider the following steady, three dimensional velocity field in Cartesian coordinates. V =…

A: Condition for flow field be incompressible is a-24c3 = 0.

Q: Find the stream function associated with the two-dimensional incompressible, possible flow with…

Q: Ay j. Is this a possible case of incompres- 23 A velocity field is given by V = Axyi %3D sible flow?…

Q: An incompressible, irrotational, two-dimensional fl ow hasthe following stream function in polar…

Q: Consider the following steady, three-dimensional velocity field in Cartesian coordinates: V-› = (u,…

A: Given Data: The given velocity vector is V→=axz2-byi→+cxyzj→+dz3+exz2k→ The condition for the flow…

Q: Fluid mechanics, I need solutions in 15 minutes please. MCQ/Determine the horizontal and vertical…

Q: Consider a flow through a nozzle, as shown in the figure below: P"Pm - 50 mis 4- 0.02 m² Streamline…

A: Continuity equation is based on the conservation of mass. If a pipe having area at one section is…

Q: Define and briefly explain the_terms listed below, support your elaboration with mathematical…

A: Required: 1. Viscous flow, inviscid flow, compressible and incompressible flow2. Laminar flow,…

Q: Assume an inviscid, incompressible flow. Also, standard sea level density and pressure are 1.23…

A: Given: An inviscid and incompressible flow ρ=1.23 kg/m3P=1.01×105N/m2 To find: if velocity V∞ is…

Q: The equation of streamlines is:

Q: Consider a flow field represented by the stream function ψ = (4+ID) x3y - (6+ID) x2y2 + (4+ID) xy3.…

A: It is a point function. It is a scalar function. It is defined for 2-D incompressible flow. If…

Q: Theodore von Kármán in 1930 theorized that turbulentshear could be represented by τturb = ε du/dy,…

A: As we know that turbulence shear stress at the wall is equal to the wall shear stress. τturb=τw…

Q: HW2_Q3. Streamline. For the velocity field v*= 4i + where A = 2m?s', and the coordinates are…

Q: The flow pattern in bearing lubrication can be illustrated by Fig. P4.83, where a viscous oil (p, µ)…

A: The boundary conditions for the given pattern of the bearing lubrication can be determined from its…

Q: (a) Use the y-momentum equation to show that the pressure gradient across the boundary layer is…

Q: Imagine a steady, two-dimensional, incompressible flow that is purely radial in the xy- or r?-plane.…

A: The incompressible continuity equation in terms of cylindrical coordinates is given by,…

Q: In his study of the circular hydraulic jump formed by afaucet fl owing into a sink, Watson proposed…

A: Given: The volume flow rate is Q. The density of the fluid is ρ. The viscosity of the fluid is μ.…

Q: The bottom of a river has a 4-m-high bump that approximates a Rankine half-body, as in Fig. The…

A: Given data: Pressure, PB = 130 kPa = 130×103 Pa Velocity, VB = 2.5 m/s Bump at A, ZA=2 m Determine:…

Q: 1. The Stokes-Oseen formula for drag force Fon a sphere of diameter D in a fluid stream of low…

A: The dimensions of the drag force is as follows: F=kg·ms2F=MLT2F=MLT-2 The dimensions of 3πμDV is as…

Q: In studying sand transport by ocean waves, A. Shields in1936 postulated that the threshold…

A: Shear stress depends on gravity, particle size, density of the particle, density of water, and…

Q: Algebraic equations such as Bernoulli's relation, Eq. (1) of Ex. 1.3, are dimensionally consistent,…

A: The x-momentum boundary layer equation derived by Ludwig Prandtl is given as,…

Q: An instrument used to measure the airspeed on many early low speed airplanes during the 1910-1930…

Q: uestion 1. For incompressible flow, the two dimensional stream function is given, P = 7r² sin(20) +…

A: Given that ; φ=7r2sin2θ+θr=4θ=π2rad

Q: The following rheological data were collected on a new "Thick 'n Spicy" brand of tomato catsup at…

A: To Plot: The values in graph and classify the fluid. Given: The rheological data is shown below:…

Q: what are velocity components,potential function and stream function?…

A: Stream Function→ for 2D flow and 3D axial symmetric flows stream functions are defined. stream…

Q: Water flows through a two-dimensional narrowing wedgeat 9.96 gal/min per meter of width into the…

A: Given data: The flow rate, Q̇ = 9.96 gal/min. The width of the wedge, b = 1 m. Write the…

Q: What is Buckingham's л-theorem? How many new dimensionless numbers can be formed from the variables…

A: In this problem, it is asking about Buckingham's pi theorem and also number of dimensionless numbers…

Q: For the pitot-static pressure arrangement of Fig.,the manometer fluid is (colored) water at 20°C.…

A: Given:Density of air at 20o C, ρ=1.2 kg/m3Dynamic viscocity of air, μ=1.8×10-5 kg/m.sFor water at…

Question

Discuss Newton's second law (the linear momentum rela-
tion) in these three forms:
Σr-mΣr-
(mV)
na
dt
Er -_Vpav)
Vpdv)
'system
Are they all equally valid? Are they equivalent? Are some
forms better for fluid mechanics as opposed to solid
mechanics?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. Given that the density of the fluid does not vary spatially and changes only with time, what differential equa9on for the density, ⍴(t), must be satisfied for this scenario to represent a physical, compressible flow field?
Consider the steady, two-dimensional, incompressible velocity field, V-› = (u, ?)=(ax + b) i-› + (−ay + c) j-›, where a, b, and c are constants. Calculate the pressure as a function of x and y.
Consider the steady, two-dimensional velocity field given by V-› = (u, ?) = (1.6 + 2.8x) i-› + (1.5 − 2.8y) j-›. Verify that this flow field is incompressible.
Consider the following steady, two-dimensional velocity field: V-›= (u, ? ) = (a2 − (b − cx)2) i-›+ (−2cby + 2c2xy) j-›Is there a stagnation point in this flow field? If so, where is it?
Define variable flow? Also discuss the forces encoundered in fluid mechanics?
A curved blood vessel has an internal diameter ? = 5 mm and a radius of curvature of ?? = 17 mm. Blood has a density of ρ = 1060 kg/m3 and a viscosity of 3.5 cP, and travels at an average velocity of ? = 1 m/s. a) Comment on the nature of the flow with reference to relevant non-dimensional groups. b) Can the flow be modelled using the Hagen-Poisseuile equation? If not, explain what specific assumptions are invalid. c) The viscosity of blood is measured and is shown in Figure Q2. Consider two long straight blood vessels with steady flow. The diameter of the first vessel is 5 mm and the average velocity is 6 cm/s. The internal diameter of the second vessel is 2.2 mm and the average velocity is 50 cm/s. Which vessel would you expect the Hagen-Poisseiulle equation to be more accurate in? Explain your answer (1-2 sentences).
Consider the two-dimensional incompressible velocity potentialϕ = xy + x 2 - y 2 . ( a ) Is it true that = ∆2 ϕ = 0, and, ifso, what does this mean? ( b ) If it exists, fi nd the streamfunction ψ ( x , y ) of this fl ow. ( c ) Find the equation of thestreamline that passes through ( x , y ) = (2, 1).
Water flows through a two-dimensional narrowing wedgeat 9.96 gal/min per meter of width into the paper(Fig. P4.72). If this inward flow is purely radial, find anexpression, in SI units, for ( a ) the stream function and( b ) the velocity potential of the flow. Assume onedimensionalflow. The included angle of the wedge is 45 ° .
Consider a steady velocity field given by V-› = (u, ?, w) = a(x2y + y2)i→ + bxy2 j→ + cxk→, where a, b, and c are constants. Under what conditions is this flow field incompressible?
Hint: take partial derivatives of the given shallow water equations and subtract them, e.g. d(eq2)/dx - d(eq1)/dy, and look for bits that make up vorticity, vorticity advection and divergence
Define and briefly explain the_terms listed below, support your elaboration with mathematicalequations and illustrations where necessary:1. Viscous flow, inviscid flow, compressible and incompressible flow2. Laminar flow, tubulent flow, steady and unsteady tlow3. Reynolds number and Mach number4. VIScOSty, specific gravity, specitic densityBuoyancy., centre of gravity and center of pressure. Bemoulli's equation
Imagine a steady, two-dimensional, incompressible flow that is purely circular in the xy- or r?-plane. In other words, velocity component u? is nonzero, but ur is zero everywhere. What is the most general form of velocity component u? that does not violate conservation of mass?