Question: A liquid flows down an inclined plane surface in a steady, fully developed laminar film of thickness h. Simplify the continuity and Navier-Stokes equations

A liquid flows down an inclined plane surface in a steady, fully developed laminar film of thickness h. Simplify the continuity and Navier-Stokes equations to model this flow field. Obtain expressions for the liquid velocity profile, the shear stress distribution, the volume flow rate, and the average velocity. Relate the liquid film thickness to the volume flow rate per unit depth of surface normal to the flow. Calculate the volume flow rate in a film of water h=1 mm thick, flowing on a surface b=1 m wide, inclined at 0=15 to the horizontal. u 0 = 15 h = 1 mm Width b = 1 m

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mechanical Engineering Questions!

Wall Steel bar d=5cm diameter F=500N Material thickness - t =2mm h=12cm 8mm Steel balls L=60cm

adam joins dzd partnership as one of four equal general partners. he makes a cash contribution of 8000 cash as well as property with fair market value of 30000 and 15000 mortgage to be assumed by the...

Identify their 2020 product mix and target market for a main stream Restaurant (before COVID) and write this in the top-left box of the table. This shows where they had Market Penetration Next,...

Consider steady, incompressible, and fully developed laminar flow of a viscous liquid down an incline with no pressure gradient. The velocity profile was derived in Example 5.9. Plot the velocity...

Assume the liquid film in Example 5.9 is horizontal (i.e., $\theta=0^{\circ}$ ) and that the flow is driven by a constant shear stress on the top surface $(y=h), \tau_{y x}=C$. Assume that the...

Assume the liquid film in Example 5.9 is not isothermal, but instead has the following distribution: \[T(y)=T_{0}+\left(T_{w}-T_{0} ight)\left(1-\frac{y}{h} ight)\] where $T_{0}$ and $T_{w}$ are,...

A liquid flows down an inclined plane surface in a steady, fully developed laminar film of thickness h. Simplify the continuity and NavierStokes equations to model this flow field. Obtain expressions...

A liquid flows down an inclined plane surface in a steady, fully developed laminar film of thickness h . Simplify the continuity and Navier - Stokes equations to model this flow field. Obtain...

The purpose of the exercise is to get you familiar with the analytical solution of the fluid flow equations in a fully developed case. You will see, how the equations simplify according to the...

QUESTION 2 - 12 MARKS Answer in the space provided - test booklets are available if necessary. A flat photographic film is being pulled out of a liquid bath at a velocity U at an angle away from the...

Compact Disc Player a compact disc (CD) is read from the bottom by a semiconductor laser with wavelength 790nm passing through a plastic substrate of refractive index 1.8. When the beam encounters a...

(a) What is the energy of a pendulum (L = 1.0 m, m = 0.50 kg) oscillating with an amplitude of 5.0 cm? (b) The pendulum's energy loss (due to damping) is replaced in a clock by allowing a 2.0-kg mass...

Find the following for the function f ( x ) = 5 x 3 7 x - 6 . ( a ) f ( 0 ) ( b ) f ( 1 ) ( c ) f ( - 1 ) ( d ) f ( - x ) ( e ) - f ( x ) ( f ) f ( x 1 ) ( g ) f ( 4 x ) ( h ) f ( x h )

3. A 5.00 kg object is to be given an upward acceleration of 0.30 m/s by a rope pulling straight upward on it. What must be the tension in the rope? A. 65.4 N B. 45.2 N C. 50.5 N D. 38.7 N

Part 1: Starch-iodine complex As we observed in Lab 2, iodine binds with starch to form a deep blue-black complex: iodine + starch starch-iodine complex Place 50 mL of water into one of your...

2. A projectile is fired with a horizontal velocity of 30m/s from the top of a cliff 80m high. How far from the foot of the cliff will it strike? A. 112 m B. 230 m C. 121 m D. 151 m

The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set. 2, 6, 15, 5, 14,...

In a random sample of six mobile devices, the mean repair cost was $60.00 and the standard deviation was $12.00. Assume the population is normally distributed and use a t-distribution to find the...

Income received in advance is shown as: A) Asset B) Liability C) Revenue D) Equity i need help

A particular steam boiler must be filled with 7.57 m 3 (2000 US gallons) of water before being used. It is connected to the water supply by copper tubing 15 m long that has a diameter of 2.60 cm. The...

Suppose that a small sphere of radius R rotates at angular velocity in a large container of otherwise static fluid. The radius and velocity are such that With the sphere rotating about the z axis,...

Liquid uptake by porous media is typically driven by surface tension. Suppose that a long, horizontal pore of radius a is initially filled with air, and that at t = 0 one end is immersed in a liquid....

Goose Corporation, a C corporation, incurs a net capital loss of $12,000 for 2016. It also has ordinary income of $10,000 in 2016. Goose had net capital gains of $2,500 in 2012 and $5,000 in 2015. a....

Cynthia, a sole proprietor, was engaged in a service business and reported her income on the cash basis. On February 2, 2016, she incorporates her business as Dove Corporation and transfers the...

Gull Corporation, a cash method, calendar year C corporation, was formed and began business on November 1, 2016. Gull incurred the following expenses during its first year of operations (November 1,...