Consider a viscous film of liquid draining uniformly down the side of a vertical rod of radius a, as in Fig P4 84 At some distance down the rod the film will approach a terminal or fully developed draining flow of constant outer radius b, with upsilon z upsilon z(r), upsilon theta upsilon r 0 Assume that the atmosphere offers no shear resistance to the film motion Derive a differential equation for upsilon z, state the proper boundary conditions, and solve for the film velocity distribution How does the film radius b relate to the total film volume flow rate Q 0 Pa Fully developed region Film U,

Question: Consider a viscous film of liquid draining uniformly down the side of a vertical rod of radius a, as in Fig. P4.84. At some distance

Consider a viscous film of liquid draining uniformly down the side of a vertical rod of radius a, as in Fig. P4.84. At some distance down the rod the film will approach a terminal or fully developed draining flow of constant outer radius b, with υz = υz(r), υθ = υr = 0. Assume that the atmosphere offers no shear resistance to the film motion. Derive a differential equation for υ z, state the proper boundary conditions, and solve for the film velocity distribution. How does the film radius b relate to the total film volume flow rate Q?

Consider a viscous film of liquid draining

0 Pa Fully developed region Film U,

Step by Step Solution

★★★★★

3.37 Rating (150 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

With vz fcnr only the NavierStokes zmomentum relation is or 1 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

E-ME-FM (518).docx

120 KBs Word File

Students Have Also Explored These Related Mechanical Engineering Questions!

A viscous film drains uniformly down the side of a vertical rod of radius R. At some distance down the rod, the film approaches a terminal or fully developed flow such that the film thickness, h, is...

Derive the differential equation for a motor driving a load through a gear system as shown in Figure, which relates the angular displacement of the load with time. the answer is Gear ratio Motor Load...

Using the loop rule, derive the differential equation for an LC circuit (Eq.31-11).

What is the dimensionless Schmidt number a function of? Select one: a. liquid density, liquid velocity, diameter of pipe and liquid viscosity O b. mass transfer co-efficient, length of a flat plate...

. Consider a laminar film of condensate flowing down a vertical wall, and assume that this liquid film constitutes the sole heat transfer resistance on the vapor side of the wall. Further assume that...

a) To find the equilibrium points of the system, we set the time derivative of the angular velocity, w, to zero: w + bw + = = = (a^2 When w o, the second and third terms on the left-hand side of the...

Consider a liquid film flow on an inclyed flat plate. Assume that the thickness ( ) of the liquid Im is constant, and the flow is two dimensional, laminar, viscous, steady, parallel and fully...

Need help with this question, thanks. Consider a thin film of magnesium fluoride MgF2 (nMgF2 = 1.38) on top of a sheet of glass (n, = 1.52). Light comes in at an angle 0. Part of the light is...

Determine the maximum flow rate of water through the horizontal 1 - c m diameter system shown below, if a maximum pressure drop of 2 - atm is allowable between oulet and inlet. The 0 . 5 - m packed...

SPH4U-07: Vie\\ X Microsoft Word X *1624382352-U X *1624382352-U X *waves test.pdf X Homework Hel X G How can light i x + V X C @ File |...

Which one of the following is the largest mass? A) 7.6 x 10* mg B) 7.6 x 107 ng C) 7.6 x 10-2 kg D) 7.6 x 10 ug

Construct the specific energy and specific force curves for a 3-ft -wide rectangular concrete channel (4.5 ft high) that carries 48 cfs.

Find D ( 5 x + 3 y ) d A where D = { ( x , y ) | x 2 + y 2 1 , x 0 } Find D ( 5 x + 3 y ) d A where D = { ( x , y ) | x 2 + y 2 1 , x 0 }

National Bank has several departments that occupy both floors of a two-story building. The departmental accounting system has a single account, Building Occupancy Cost, in its ledger. The types and...

How many grams of Na2HPO4.2H2O should be added to 100 milliliter and 0,2 molarity of H3PO4 for the buffer solution pH 7.30? Molar mass of Na2HPO4.2HaO= 178 gram For H3PO4 ; Ka1= 7,11x10^-3...

A survey asked, "How important is it to you to buy products that are made in America?" Of the 400 Americans surveyed, 150 responded, "It is not important." Find the sample proportion. Round the...

The pH in your cells is decreasing Cells have buffers to minimise changes in pH Briefly explain what the buffer would do in this situation with respect to the H concentration in your cells?

8. P P When possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth value. If the truth value of the statement...

Your employer has asked you to examine the interest-rate risk of your bank relative to your direct competition. Management is concerned that interest rates will fall by the end of the year and wants...

QUESTION ONE Chanda Mulenga, an investor, is interested in evaluatingg the performance of three portfolio managers. He obtained the following data: Manager Portfolio Return Portfolio Standard...

b) Ravindran has been depositing money at the end of each year into an account drawing 6.5% compound interest per annum. Calculate the balance in the account at the end of year four if he deposited...