Any 10 examples of dot product and any 10 examples of cross product for physics

A spherical thermocouple junction 1.0 mm in diameter is inserted in a combustion chamber to measure the temperature ?T? of the products of combustion. The hot gases have a velocity of V= 5 m/s. (a) If the thermocouple is at room temperature, Ti,when it is inserted in the chamber, estimate the time required for the temperature difference, ?T?-T, to reach 2% of the initial temperature difference, ?T?-Ti. Neglect radiation and conduction through the leads. Properties of the thermocouple junction are approximated as k= 100 W/m·K, c=385 J/kg·K, and ?=8920 kg/m³, while those of the combustion gases may be approximated as k=0.05 W/m·K, ?=50 x 10^-6 m²/s, and Pr=0.69.

(b) If the thermocouple junction has an emissivity of 0.1 and the cooled walls of the combustor are at Tc=400 K, what is the steady-state temperature of the thermocouple junction if the combustion gases are at 1000 K? Conduction through the lead wires may be neglected.

Assuming that the gas properties are constant, what is the value of the Nusselt number?

What is the average convection heat transfer coefficient for the gas flowing over the thermocouple, in W/m²·K?

What is the Biot number for this problem?

How long does it take for the temperature difference (?T?-T) to get within 2% of the initial temperature difference (?T?-Ti), in s?

What is the final steady state temperature of the thermocouple, in K, if the combustion gases are at 1000 K?

In a porter governor, the upper and lower arms are each 220m long, and aare each inclined at 30degrees to the vertical when the sleeve is in its lowest position. the points of suspension are each 40 mm from the axis of the spindle. The mass of each of the three rotating balls is 3kg and that of the central load on the sleeve is 30kg. if the movement of the sleeve is 36 mm, find the range of speed of the governor. Neglect friction.

A long wire of diameter D = 2mm is submerged in an oil bath at 25 degrees C. The wire has an electrical resistance per unit length of R’ = 0.015 Ω/m. If a current of I = 75A flows through the wire and the convection coefficient is h = 400 W/m2*K, what is the steady-state temperature of the wire? From the time the current is applied, how long does it take for the wire to reach a temperature that is within 1-degree C of steady-state? The wire properties are p = 7800 kg/m3, c = 500 J/kg*K, and k = 25 W/m*K.

The function Sine is defined as:

where x is an angle in radians

Write a Matlab script program to compute the sinus value of any angle as the following:

- The program should run always until the user enters - 1 to exit from the program.

- A sk user to enter: Number of elements (N) that should be included in the sum

- C heck that N is a positive integer . [ Hint: use ( round (N) - N) or mod(N,1) ]

- A sk user to select to enter the angle, X , in degrees or radians

- A sk user to enter the value of X , it could be scalar or vector .

- Using switch/if and loops, calculate the value of sin(X).

- P rint the angle in degrees, the equivalent angle in radians and the sinus value for this angle.   

Given that a potential of 0.25 mV is applied to an aluminum conductor that is 100?m long and has a square cross–sectional area with width 1?m, answer the following questions. The resistivity of aluminum is 25 nW×m.

(a)Calculate the electric field.

(b)Calculate the magnitude of the current flowing in the conductor.

(c)Calculate the resistance of the conductor.

We are learning about the properties of materials right now. Thanks in advance.

countershaft in Prob. 3–72, p. 152, is part of a speed reducing compound gear train using
20° spur gears. A gear on the input shaft drives gear A. Gear B drives a gear on the output
shaft. The input shaft runs at 2400 rev/min. Each gear reduces the speed (and thus increases
the torque) by a 2 to 1 ratio. All gears are to be of the same material. Since gear B is the
smallest gear, transmitting the largest load, it will likely be critical, so a preliminary analysis
is to be performed on it. Use a diametral pitch of 2 teeth/in, a face-width of 4 times the circu-
lar pitch, a Grade 2 steel through-hardened to a Brinell hardness of 300, and a desired life of
15 kh with a 95 percent reliability.

1) if b is meshing with another gear with a diameter d=16 in what would be the required teeth on Fb?

2)Determine factors of safety for pitting

GD&T

Explain followings:

1. Dimention placement in multiview drawings

2. General arrangement of dimensions in multuview drawings

3. Dimension system

What do you think are the advantages and disadvantages of isothermal constant volume high extension cycle? And how efficient do you think it can be?

A thick spherical pressure vessel of inner radius 150 mm is subjected to maximum an internal pressure of 80 MPa. Calculate its wall thickness based upon the (a) principal stress theory, and (b) total strain energy theory. Poisson's ratio = 0-30, yield strength 300 MPa.

please answer only if you know correctly.

Diffusion in material

You are hardening a very thick tool plate made of BCC Fe by increasing the carbon concentration in its surface layer by heating the tool in the presence of a C-rich gas (e.g. methane) which maintains a constant C concentration at the surface. A heat treatment at 600 °C for 100 minutes results in a C concentration of 0.75 wt% at a position 0.5 mm below the surface. How long would it take to obtain the same result (i.e. the same C concentration at the same depth) if the heat treatment were conducted at 900 °C. Schematically draw the C concentration profile (i.e. the C composition as a function of the distance from the surface) in the tool plate. At either of the temperatures, does the diffusion rate (measured by the diffusion flux) go up or down with increasing distance from the surface and why?

D₀ = 2 x 10^-6 m²/s and Q_d = 84 kJ/mol

What is the difference between a vane compressor and a radial compressor?

Geometric Dimensionig and Tolerancing

1. Professions (desiner, manufacturing engineer, machinist, machine programmer, inspector, tool designer) and trades, that how affected by dimentions?

2. How to reduces cost? by design through teamwork (inspector, machinist, engineer)

Kate deposits P5,000 to her bank account every year when she was in high school for four years to prepare for her college degree. She took an engineering course and since then, she stopped depositing to her bank account. Right after graduation (she graduated on time), she got a job that pays P250,000 a year. If she continues to deposit to the same bank account P50,000 every year for 10 years, calculate the future worth after 30 years if the deposits are made at the end of each year and the bank pays 2% interest per year

Search the Internet and locate a job posting from a Part 121 or 135 carrier. After locating your position, read and review the required maintenance organization management positions in AC 120-16F, Chapter 4. How does the position and job description that you identified align with one of the required positions in the advisory circular? How does it differ?