samplequiz_sol

A constant-thickness film of viscous liquid flows in laminarmotion down a plate inclined at angle θ , as in Fig. P4.36.The velocity profile isu = Cy(2h - y) υ = w = 0Find the constant C in terms of the specifi c weight andviscosity and the angle θ . Find the volume fl ux Q per unitwidth in terms of these parameters.

Q1: The U tube (in Fig.1) is open at (D) and closed in (A). What will be the pressure at point (A, B and C): 1- Uniform acceleration (az=10m/sec?) to the top only. 2- Uniform acceleration (ax =10m/sec²) to the right and (az=10m/sec") to the top. 0.6m 0.9m Fig.1

A piston compresses gas in a cylinder by moving at constantspeed V , as in Fig. P4.18. Let the gas density andlength at t = 0 be ρ 0 and L 0 , respectively. Let the gas velocityvary linearly from u = V at the piston face to u = 0 atx = L . If the gas density varies only with time, fi nd anexpression for ρ ( t ).

Consider a sphere of radius R immersed in a uniform stream Uo, as shown in Fig. P4.7. According to the theory of Chap. 8, the fluid velocity along streamline AB is given by V = ui = U, (1+ Find (a) the position of maximum fluid acceleration along AB and (b) the time required for a fluid particle to travel from A to B. B(Sphere *=-4R P4.7

A horizontal circular jet of air (pair plate as shown below. The air jet has a velocity V; = 60 m/s and the air jet has a diameter Dj = 40 mm. An anchoring force FA is holding the plate in its stationary position. This entire system is open to the atmosphere. 1.23 kg/m³) strikes a stationary flat Gravity is into / out of the page ... gravity will not be important here! The air velocity magnitude remains constant ( |Vi| = |V2| = |V3| ) as the air flows across the plate surface (this means there are no shear stress effects). Hint align your coordinate system with V3, V2, and FA. ... V2 D : = 40 mm V; = 40 m/s 30° V3 FA (3.a) What is the magnitude [ N ] of the anchoring force FA? (3.b) What fraction [ % ] of the total mass of air leaves at V2? Now we will change the problem a little. Allow the plate to move to the right with a constant speed of 18 m/s. You should realize that this will mean that the anchoring force is reduced from the answer you found in (4.a). Please place your observer…

U L CD Fig.1. Airflow on a cylinder U U U/2 L/2 L/2 1. When a uniform stream flows past an immersed thick cylinder, a broad low-velocity wake is created downstream, idealized as a V shape in Fig. 1. Pressures p1 and p2 are approximately equal. (a) If the flow is two-dimensional and incompressible, with width b into the paper, derive a formula for the drag force F on the cylinder. (b) Rewrite your result in the form of a dimensionless drag coefficient based on body length F pU²bL

Q2): Consider flow of an incompressible fluid of density p and viscosity u through a long, horizontal section of round pipe of diameter D. The velocity profile is V. A surface tension a. Develop a non-dimensional relationship between surface tension o and the other parameters in the problem.

.3 2. 1. If u = 3x*yt and v = -6x°y´t“ answer the following questions giving reasons, Is this flow or fluid: (a) Real (Satisfies Continuity Principle). (b) Steady or unsteady. (c) Uniform or non-uniform. (d) One, two, or three dimensional. (e) Compressible or incompressible. Also, Find the acceleration at point (1,1).

3. A cylinder of radius r; rotates at a speed w coaxially inside a fixed cylinder of radius r,. A viscous Newtonian fluid fills the space between the cylinders. a) Determine the velocity profile in the space between the cylinders b) Determine the shear stress on the surface of each cylinder. Are the shear stresses equal? Explain. c) Assume that the fluid is glycerin at room temperature. The cylinders are 25 cm tall, r; = 9 cm, cylinder at one full rotation every 10s. and 10 cm. Calculate the torque required to steadily turn the inner %D

Oil, of density ρ and viscosity μ , drains steadily down theside of a vertical plate, as in Fig. P4.80. After a developmentregion near the top of the plate, the oil fi lm willbecome independent of z and of constant thickness δ .Assume that w = w ( x ) only and that the atmosphere offersno shear resistance to the surface of the fi lm. ( a ) Solve theNavier-Stokes equation for w ( x ), and sketch its approximateshape. ( b ) Suppose that fi lm thickness δ and the slopeof the velocity profi le at the wall [ ∂ w /∂ x ] wall are measuredwith a laser-Doppler anemometer (Chap. 6). Find anexpression for oil viscosity μ as a function of ( ρ , δ , g ,[ ∂ w / ∂ x ] wall ).

An incompressible fluid (kinematic viscosity, 7.4 x10-7 m²/s, specific gravity, 0.88) is held between two parallel plates. If the top plate is moved with a velocity of 0.5 m/s while the bottom one is held stationary, the fluid attains a linear velocity profile in the gap of 0.5 mm between these plates; the shear stress in Pascals on the surface of top plate is rt of this book may be repro

Q.2 3 A fluid of density 1200 kg/m at 1 atm pressure is compressed to 101 atm pressure isothermally. If the isothermal -5 compression is 4.8x 10 atm, the -1 increase in density in kg/m of fluid is

Fluid Kinematic Assignment HW; D, =450 mm, D2=300 mm, D3= 225 mm, D= 150 mm V,=1.8 m/s V3= 3.6 m/s Find the values of the below; 3 %3D 1 4 1- Q,, 2- Q2, 3- Q4» 4- Q3, 5- V, & 6- V4

The flow pattern in bearing lubrication can be illustrated by Fig. P4.83, where a viscous oil (p, µ) is forced into the gap h(x) between a fixed slipper block and a wall moving at velocity U. If the gap is thin, h< L, it can be shown that the pressure and velocity distributions are of the form p = p(x), u = u(y), v = w = 0. Neglecting gravity, reduce the Navier-Stokes rquations .. to a single differential equation for u(y). What are the proper boundary conditions? Integrate and show that 1 dp ( – yh) + U( и 2д dx where h = h(x) may be an arbitrary, slowly varying gap width. ( Oil inlet Fixed slipper block Oil outlet ho h(x) и (у) Moving wall

An excellent approximation for the two-dimensional incompressible laminar boundary layer on the flat surface in Fig. P4.17 is for y s8 where 8 = Cx2, C = const (a) Assuming a no-slip condition at the wall, find an expression for the velocity component v(x, y) for ys 8. (b) Then find the maximum value of vat the station x = 1 m, for the particular case of airflow, when U = 3 m/s and &= 1.1 cm. Layer thickness 5(x) U= constant и (х, у) u(x, y)

Consider a viscous fi lm of liquid draining uniformly downthe side of a vertical rod of radius a , as in Fig. P4.84. Atsome distance down the rod the fi lm will approach a terminalor fully developed draining fl ow of constant outer radiusb , with υ z = υ z ( r ), υ θ = υ r = 0. Assume that the atmosphereoffers no shear resistance to the fi lm motion. Derivea differential equation for υ z , state the proper boundaryconditions, and solve for the fi lm velocity distribution.How does the fi lm radius b relate to the total fi lm volumefl ow rate Q ?

A belt moves upward at velocity V, dragging a fi lm ofviscous liquid of thickness h , as in Fig. . Near the belt,the fi lm moves upward due to no slip. At its outer edge, thefi lm moves downward due to gravity. Assuming thatthe only nonzero velocity is υ ( x ), with zero shear stress atthe outer fi lm edge, derive a formula for ( a ) υ ( x ), ( b ) the average velocity V avg in the fi lm, and ( c ) the velocity V c forwhich there is no net flow either up or down. ( d ) Sketchυ ( x ) for case ( c ).

P3.5 Water at 20°C flows through a 5-in-diameter smooth pipe at a high Reynolds number, for which the velocity profile is approximated by u = U.(v/R)/8, where U, is the cen- terline velocity, R is the pipe radius, and y is the distance measured from the wall toward the centerline. If the cen- terline velocity is 25 ft/s, estimate the volume flow rate in gallons per minute.

When a person ice skates, the surface of the ice actuallymelts beneath the blades, so that he or she skates on a thinsheet of water between the blade and the ice.( a ) Find an expression for total friction force on the bottomof the blade as a function of skater velocity V , bladelength L , water thickness (between the blade and theice) h , water viscosity μ , and blade width W .( b ) Suppose an ice skater of total mass m is skatingalong at a constant speed of V 0 when she suddenlystands stiff with her skates pointed directly forward,allowing herself to coast to a stop. Neglecting frictiondue to air resistance, how far will she travelbefore she comes to a stop? (Remember, she iscoasting on two skate blades.) Give your answer forthe total distance traveled, x , as a function of V 0 , m ,L , h , μ , and W .( c ) Find x for the case where V 0 = 4.0 m/s, m = 100 kg,L = 30 cm, W = 5.0 mm, and h = 0.10 mm. Do youthink our assumption of negligible air resistance is agood one?

For the pressure-gradient fl ow between two parallel platesof Fig. 4.12( b ), reanalyze for the case of slip fl ow at bothwalls. Use the simple slip condition u wall = l( du / dy ) wall ,where l is the mean free path of the fl uid. ( a ) Sketch theexpected velocity profi le. ( b ) Find an expression for theshear stress at each wall. ( c ) Find the volume fl ow betweenthe plates.

SAE 10 oil at 20 ° C fl ows between parallel plates 8 mmapart, as in Fig. P4.86. A mercury manometer, with wall pressure taps 1 m apart, registers a 6-cm height, as shown.Estimate the fl ow rate of oil for this condition.

A storage tank, 26 ft in diameter and 36 ft high, is fi lledwith SAE 30W oil at 20 ° C. ( a ) What is the gage pressure,in lbf/in 2 , at the bottom of the tank? ( b ) How does your resultin ( a ) change if the tank diameter is reduced to 15 ft?( c ) Repeat ( a ) if leakage has caused a layer of 5 ft of waterto rest at the bottom of the (full) tank.

1. 2. If the gravitational force of the earth decreases, the most likely scenario(s) is (are): (1) (11) The iceberg will have a larger portion exposed above the sea level since its weight will be lower. The atmosphere is likely to be thinner as air molecules will find it easier to escape to outer space. (11) (111) (A) (B) (C) (D) (i) To solve a fluid dynamic problem completely, it must generally satisfy: (i) Conservation of mass. Conservation of momentum. Conservation of energy. (A) (B) (C) (D) (ii) (i) and (ii) None of the above (i) (11) (111) All of the above