A viscous incompressible fluid is between two parallel plates (that are along the x-z plane), one of them is at y = 0 and the other at y = d.

1. a) Considerthecasewheretheflowisstationaryinthezˆdirection, driven by a pressure gradient. Write down the Navier-Stokes equations and solve for the velocity field after imposing the relevant boundary conditions. [10 points]

2. b) The pressure gradient is now removed, but the plate at y = d is moved in an oscillatory fashion with velocity ue−iωt in the zˆ direction, while the other plate remains stationary. Write down the Navier-Stokes equations and solve for the velocity field after imposing the relevant boundary conditions. [15 points]

An open container holds ice of mass 0.560 kg at a temperature of -19.6 ∘C . The mass of the container can be ignored. Heat is supplied to the container at the constant rate of 760 J/minute . The specific heat of ice to is 2100 J/kg⋅K and the heat of fusion for ice is 334×103J/kg.

a. How much time tmelts passes before the ice starts to melt?

b. From the time when the heating begins, how much time trise does it take before the temperature begins to rise above 0∘C?

The volume of an ideal gas is held constant. Determine the ratio P2/P1 of the final pressure to the initial pressure when the temperature of the gas rises (a) from 51 to 102 K and (b) from 23.7 to 64.4 oC. (a) P2/P1 = Number Units (b) P2/P1 = Number Units

7. The evaporation of water cools the surroundings, and the condensation of this vapor
   1. Does nothing
   2. Warms the surroundings
   3. Increases the value of the latent heat of vaporization
   4. Decreases the value of the latent heat of vaporization

8. The heat involved in the change of phase form solid ice to liquid water is
   1. Latent heat of vaporization
   2. Latent heat of fusion
   3. Latent heat of condensation
   4. None of the above
9. More molecules are returning to the liquid state than are leaving the liquid state. This process is called
   1. Boiling
   2. Freezing
   3. Condensation
   4. Melting
10. The temperature of a gas is proportional to the
    1. Average velocity of the gas molecules
    2. Internal potential energy of the gas
    3. Number of gas molecules in a sample
    4. Average kinetic energy of the gas molecules
11. The specific heat of soil is 0.2 cal/g⁰C, and the specific heat of water is 1 cal/g⁰C. This means that if 1 kg of soil and 1 kg of water each receives 1 kcal of energy, ideally,
    1. The water will be warmer than the soil by 0.8 ⁰C
    2. The soil will be 4 ⁰C warmer than the water
    3. The soil will be 5 ⁰C warmer than the water
    4. The water will warm by 1 ⁰C, and the soil will warm by 0.2 ⁰C
12. Styrofoam is a good insulating material because
    1. It is a plastic material that conducts heat poorly
    2. It contains many tiny pockets of air
    3. Of the structure of the molecules that make it up
    4. It is not very dense
13. As a solid undergoes a phase change to a liquid, it
    1. Releases heat while remaining at a constant temperature
    2. Absorbs heat while remaining at a constant temperature
    3. Releases heat as the temperature decreases
    4. Absorbs heat as the temperature increases
14. Which of the following contains the most heat
    1. A bucket of water at 0⁰C
    2. A barrel of water at 0⁰C
    3. Neither contains ay heat since the temperature is zero
    4. Both have the same amount of heat
15. Conduction best takes place in a
    1. Solid
    2. Fluid
    3. Gas
    4. Vacuum
16. Convection best takes place in a(an)
    1. Solid
    2. Fluid
    3. alloy
    4. Vacuum
17. The phase change from ice to liquid water takes place at
    1. Constant pressure
    2. Constant temperature
    3. Constant volume
    4. All of the above
18. Which of the following has the greatest value for liquid water?
    1. Latent heat of vaporization
    2. Latent heat of fusion
    3. Both are equivalent
    4. None of the above is correct

Two streams merge to form a river. One stream has a width of 8.4 m, depth of 3.5 m, and current speed of 2.1 m/s. The other stream is 6.4 m wide and 3.1 m deep, and flows at 2.5 m/s. If the river has width 10.5 m and speed 2.8 m/s, what is its depth? Clearly explain why the Volume Flow rate R, (the volume of fluid per second that passes a point in a flow), is equal to the cross sectional area times the velocity. R = Av

In the figure, a solid cylinder of radius 16 cm and mass 7.7 kg starts from rest and rolls without slipping a distance L = 4.4 m down a roof that is inclined at angle θ = 32°. (a) What is the angular speed of the cylinder about its center as it leaves the roof? (b) The roof's edge is at height H = 5.3 m. How far horizontally from the roof's edge does the cylinder hit the level ground?

consider two cubes: a copper cube (Density = 8.96 g/cm^3) and a lead cube (Density = 11.4 g/cm^3) that both have an edge length of 3.0 cm.

1) which cube (if either) has the greater mass? How do you know?

2) which cube (if either) displaces the more water when fully submerged? how do you know?

3) which cube (if either) experiences the buoyant force of greatest magnidude when fully submerged? How do you know?

4) calculate the magnitude of the buoyant force (in Newtons) acting on the copper cube and the lead cube when each is fully submerged in water. Show your work!

5) If either block is immersed only half-way into the water, how does the magnitude of the bouyant force in this case compare to the buoyant force when that same block is fully submerged? Defend your answer.

Plase show all work. Thank you so much.

I need the steps for this problem. If a runner (perpendicular area = 0.6 m2; fluid density = 1.14 kg/m3; Cd = 0.5) completes a marathon (26.2 miles) in three hours, while running against a 10-mph headwind throughout the race, how much more work will she have performed against the air, relative to completing the marathon in the same time on a still day (no wind)? Answer: ~395 KJ

In the plumbing of an old house water enters a copper pipe of 1 inch diameter and with a flow rate of 0.25 gal/s.

A) After several bends the pipe reaches a joint where the diameter is reduce to 3/4 inches. What is the flow rate of water in this constricted section of pipe?

B) In Which section of the pipe is the water pressure greater , where the diameter is 1 inch or 3/4 inches ?

n = 4.67 mol of Hydrogen gas is initially at T = 345.0 K temperature and p_i = 3.02×10⁵ Pa pressure. The gas is then reversibly and isothermally compressed until its pressure reaches p_f = 6.72×10⁵ Pa. What is the volume of the gas at the end of the compression process?

How much work did the external force perform?

How much heat did the gas emit?

How much entropy did the gas emit?

What would be the temperature of the gas, if the gas was allowed to adiabatically expand back to its original pressure?

You decide to roll a 0.15-kg ball across the floor so slowly that it will have a small momentum and a large de Broglie wavelength. A.If you roll it at 1.2×10−3 m/s , what is its wavelength? B.How does this compare with the de Broglie wavelength of the high-speed electron that strikes the back face of one of the early models of a TV screen at 1/10 the speed of light (2.4×10−11m)?

(a) Explain what is a Gyroscopie ratio. (b) Using the Gyroscopie ratio for 1H, Calculate the Lamor frequency for 21T NMR magnet. (c) Why HTS magnet (insert magnet) is necessary to build up beyond 1-GHz NMR magnet system?

A hollow sphere of radius 0.190 m, with rotational inertia I = 0.0218 kg·m² about a line through its center of mass, rolls without slipping up a surface inclined at 10.8° to the horizontal. At a certain initial position, the sphere's total kinetic energy is 7.90 J. (a) How much of this initial kinetic energy is rotational? (b) What is the speed of the center of mass of the sphere at the initial position? When the sphere has moved 0.600 m up the incline from its initial position, what are (c) its total kinetic energy and (d) the speed of its center of mass?