Consider laminar steady boundary layer at a flat plate. Assume the velocity profile in the boundary layer as parabolic, u(y)=U(2 (y/δ)-(y/δ)^2).

1. Calculate the thickness of the boundary layer, δ(x), as a function of Reynold's number.

2. Calculate the shear stress at the surface, τ, as a function of Reynold's number.

Re=ρUx/μ

The Equation of motion for the standard mass-spring-damper system is

Mẍ + Bẋ + Kx = f(t).

Given the parameters {M = 2kg, B = 67.882 N-s/m, K = 400 N/m}, determine the free response of the system to initial conditions { x₀ = -1m, v₀ = 40 m/s}. To help verify the correctness of your answer, a plot of x(t) should go through the coordinates {t, x(t)} = {.015, -0.5141} and {t, x(t)} = 0.03, -0.2043}.

determine the steady-state response of the system to sinusoidal inputs of unit amplitude at specified frequencies. You may use any initial conditions you wasn’t for this section. Use the following frequencies: ω = {0.2, 1, 6, sqrt (200), 20, 100, 1000} rad/s.

Modify your Matlab code to numerically simulate the response of the system to the frequencies listed above. Simulate one frequency at a time. Simulate for a sufficient time that the system will have attained steady state. Plot three periods of the systems’s response at steady state (so the initial time value on the plot will not be t = 0). Then estimate the amplitude of the response for each frequency; you should have seven amplitudes when you are done.

Make a second plot where you plot the amplitudes determined above against the frequencies (make a frequency response magnitude plot). The x-axis should be logarithmic and the y-axis should be in dB. CLEARLY LABEL YOUR AXES. For the plot, connect the points with solid black lines with a LineWidth of 3.

Evaluate │H(jω)│ for the frequencies: ω = {0.25, 1.5, 6.5, 15, 25, 150, 800} rad/s. Do this BY HAND. Clearly show your work. Then plot the resulting {ω, │H(jω)│} points as green diamonds using Markersize of 10 and LineWidth of 3.

The Equation of motion for the standard mass-spring-damper system is

Mẍ + Bẋ + Kx = f(t).

Given the parameters {M = 2kg, B = 67.882 N-s/m, K = 400 N/m}, determine the free response of the system to initial conditions { x₀ = -1m, v₀ = 40 m/s}. To help verify the correctness of your answer, a plot of x(t) should go through the coordinates {t, x(t)} = {.015, -0.5141} and {t, x(t)} = 0.03, -0.2043}.

Numerically simulate the response of the system using the Matlab function ode45. Plot the displacement of the mass as a function of time for the first 0.5s. Use a time-resolution of 0.001s (have ode45 return values of x(t) at 1ms intervals). This plot should be a solid black line with a LineWidth of 3.

“Hold” the plot and superimpose the two points listed above (the two {t, x(t)} pairs). Use red circles to show those points. Make the circles’ Markersize of 10 and LineWidth of 3.

Determine the exact analytic (“hand”) solution to the problem. Use Matlab to calculate the values of that solution at 0.05s time steps. Superimpose that data on top of the numerical solution (and the two red circles) using blue diamonds with the same Markersize and LineWidth parameters as for the circles.

The Equation of motion for the standard mass-spring-damper system is

Mẍ + Bẋ + Kx = f(t).

Given the parameters {M = 2kg, B = 67.882 N-s/m, K = 400 N/m}, determine the free response of the system to initial conditions { x₀ = -1m, v₀ = 40 m/s}. To help verify the correctness of your answer, a plot of x(t) should go through the coordinates {t, x(t)} = {.015, -0.5141} and {t, x(t)} = 0.03, -0.2043}.

Numerically simulate the response of the system using the Matlab function ode45. Plot the displacement of the mass as a function of time for the first 0.5s. Use a time-resolution of 0.001s (have ode45 return values of x(t) at 1ms intervals). This plot should be a solid black line with a LineWidth of 3.

“Hold” the plot and superimpose the two points listed above (the two {t, x(t)} pairs). Use red circles to show those points. Make the circles’ Markersize of 10 and LineWidth of 3.

Determine the exact analytic (“hand”) solution to the problem. Use Matlab to calculate the values of that solution at 0.05s time steps. Superimpose that data on top of the numerical solution (and the two red circles) using blue diamonds with the same Markersize and LineWidth parameters as for the circles.

A six-station rotary indexing machine performs the machining operations shown in the table below, with processing times and breakdown frequencies for each station. Transfer time is 0.15 min. A study of the system was undertaken, during which time 2000 parts were completed. The study also revealed that when breakdowns occur, the average downtime is 7.0 min. For the study period,

determine: 1) Average hourly production rate______________. 2) Line uptime efficiency______________. 3) How many hours were required to produce the 2000 parts__

(A) Give industry and household examples from your experience of devices that simplify installation and attachment, and that eliminate trial-and-error adjustment.

(B) Give examples from your experience of situations where trial-and-error adjustment could be eliminated by simple means.

A mass of 3 kg of saturated liquid-vapor mixture of water is contained in a piston-cylinder device at 175 kPa. Initially, 2 kg of the water is in the liquid phase and the rest is in the vapor phase. An electrical heater is in operation, and the piston rises until it hits a set of stops, which are set at double the initial volume. Electrical heating continues until the pressure reaches 500 kPa. Determine (a) the initial and final temperatures, (b) the mass of liquid water when the piston first hits the stops, and (c) the electrical work done during this process. Show all equations.

A mass of 3 kg of saturated liquid-vapor mixture of water is contained in a piston-cylinder device at 175 kPa. Initially, 2 kg of the water is in the liquid phase and the rest is in the vapor phase. An electrical heater is in operation, and the piston rises until it hits a set of stops, which are set at double the initial volume. Electrical heating continues until the pressure reaches 500 kPa. Determine (a) the initial and final temperatures, (b) the mass of liquid water when the piston first hits the stops, and (c) the electrical work done during this process. Show all equations.

ASSIGNMENT 1

TOPIC: INTRODUCTION OF FLUID MECHANICS

QUESTION 1: 10 MARKS

In your own words, explain what have you learnt from fluid mechanics course.

QUESTION 2: 40 MARKS

Refined crude oil has been used to lubricate moving parts in a wide variety of machines and engines. These petroleum-based lubricants are extracted from natural crude oil, and must be refined, desalted, dewaxed, and distilled from crude feedstock. However, recently, engineers are moving towards non-petroleum based lubricants or known as synthetic lubricants. Obtain information about non-petroleum based lubricants and summarize your findings in a brief report by following the format given below. The report should contain minimum 1500 words (excluding figure and table title and content, references)

QUESTION 3: 50 MARKS

It is predicted that nanotechnology and the use of nano sized objects will improvise many processes and products. Among new new nanotechnology areas is that of nano scale fluid mechanics or known as nanofluid. Fluid behavior at the nano scale can be entirely different than that for the usual everyday flows. Obtain various information of nano fluid mechanics and summarize your findings in a brief report by following the format given below. The report should contain minimum 1700 words (excluding figure and table title and content, references)

Determine the changes in length, breadth, and thickess of a steel bar which is 5m long, 40mm wide and 30mm thick and is subjected to an axial pull of 35kN in the direction of its length. Then find the volumetric strain and final volume of the given steel bar. (Take E= 200000 N/mm2 and poisson ratio (v) = 0.32)

In a manufacturing process, stainless steel cylinders (AISI 304) initially at 600K are quenched by submersion in an oil bath maintained at 300K with h=500W/m²-K. Each cylinder is of length 2L=60 mm and diameter D=80mm. Consider a time 3 min into the cooling process and determine the temperatures at the center of the cylinder, at the center of the circular face and at the mid height of the site. (Use the Heisler charts to answer these questions). You may evaluate properties at the mean temperature of T_m=450K.

A large block having the properties of a chrome brick at 200^oC is at uniform temperature of 30^oC when it is suddenly exposed to a constant surface flux of 3x10⁴ W/m². For this case, determine:

a. The temperature at a depth of 3 cm after a time of 10 min

b. The surface temperature at this time

An air compressor rapidly fills a 0.3m3 tank (there is no heat transfer through the tank walls), initially containing air at 27 ?C, 1 atm, with air drawn from the atmosphere at 27? ?C, 1 atm. During filling, the relationship between the pressure and specific volume of the air in the tank is pv1.4 = constant. You can model the air as an ideal gas with constant specific heats at 300K.

Calculate (and show your work) the tank’s pressure and temperature, and the

work input to the compressor for the case of m/m1 = 1.5, where m1 is the initial mass in the tank and m is the mass in the tank at any time after filling starts

Plot the pressure, in atm of the air within the tank versus the ratio of m/m1

Plot the temperature, in ?C, of the air within the tank versus the ratio of m/m1

Plot the compressor work input, in Btu, versus m/m1.

For all three graphs, let m/m1 vary from 1 to 3 in increments of 0.1

An air compressor rapidly fills a 0.3m3 tank (there is no heat transfer through the tank walls), initially containing air at 27 ?C, 1 atm, with air drawn from the atmosphere at 27? ?C, 1 atm. During filling, the relationship between the pressure and specific volume of the air in the tank is pv1.4 = constant. You can model the air as an ideal gas with constant specific heats at 300K.

Calculate (and show your work) the tank’s pressure and temperature, and the

work input to the compressor for the case of m/m1 = 1.5, where m1 is the initial mass in the tank and m is the mass in the tank at any time after filling starts

Plot the pressure, in atm of the air within the tank versus the ratio of m/m1

Plot the temperature, in ?C, of the air within the tank versus the ratio of m/m1

Plot the compressor work input, in Btu, versus m/m1.

For all three graphs, let m/m1 vary from 1 to 3 in increments of 0.1