10 Puan) xy + 6x + (x² – 4) y' = 0 x+ +2 O Homogenous O Seperable O Non-homogenous where M(xy) and N(x,y) are linear
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Differantial Equations
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- The dependence of thermal conductivity of a material on temperature is given by an empirical equation k = a ebT where a and b are constants, and k is in W/m-K and T is in K. Spot the true statement from the following set. a, a and b have the same dimension as k. b. a has the dimension of k and b is dimensionless. c. a and b are dimensionless. d. a has the dimension of k and b has the dimension of T.Answers (a) er=15.30-250.2/r^2 , etheta=15.30+250.2/r^2 (b) delta c = 8.12x10^-4 inThe continuity equation is not based on the principle of conservation of mass. Select one: True False
- Find the coefficient of volume expansion of argon at 150 C? 2 points a)1 b)0.0023 c)0.0077 d)0.0067 e)not sufficient informationมอเตอร์เหนี่ยวนํา 3 เฟส 50-Hz ที่เชื่อมต่อดาวโรเตอร์ให้ 500 V (r.m.s.) หยุดนิ่งระหว่างวงแหวนสลิปบนวงจรเปิด คํานวณกระแสและตัวประกอบกําลังเมื่อหยุดนิ่งเมื่อขดลวดโรเตอร์เชื่อมต่อกับวงจรภายนอกที่เชื่อมต่อกับดาวซึ่งแต่ละเฟสมีความต้านทาน 10 Ωและการเหนี่ยวนํา 0.04 H ความต้านทานต่อเฟสของขดลวดโรเตอร์คือ 0.2 Ω และการเหนี่ยวนําคือ 0.04 H. นอกจากนี้ให้คํานวณตัวประกอบกระแสและกําลังเมื่อแหวนลื่นลัดวงจรและมอเตอร์ทํางานด้วยการลื่นไถล 5 เปอร์เซ็นต์ สมมติว่าฟลักซ์คงที่ [10.67 A; 0.376; 21.95 A; 0.303||Suppose we got the following data during a test of a 2- stroke engine in which gas is usedas a fuel:Diameter of the piston = 149 mmStroke length = 179 mmClearance volume = 0.88 literrpm of the engine = 302Indicated mean effective pressure = 6.0 barGas consumption = 6.0 m3/hCalorific value of the gas (fuel) = 16990 kJ/m3Make a clear sketch the geometry of this engine using the data and determine thefollowing:i. Indicated power developed by the engine in watt.ii. Air Standard Efficiencyiii. Indicated thermal efficiency of the engine.
- Discussion: 1- Measuring the angle of phase shift for every state. set the AC voltage source 15V and using the data in the following table NO. Frequency | Capacitance | Resistance | Inductance 1 2KHZ 0.1uF 100Q 0.1mH 2 20 KHZ 0.1 yF 100 Q 0.1 mH 3 200 KHZ |0.1 pF 100 Q 0.1 mH 2- Draw the phase shift for every state as graph .5.2 Evaluate the Prandtl number from the following data: , .Give definition of unreliability F(t)of a component as function of time.
- The partial di§erential equation for the small-amplitude vibrations of a string of length ` is given by A@2y@t2T@2y@x2 = 0 where y(x; t) is the vibration amplitude, is the material density of the string, A is the string cross sectional area, and T is the tension force in the string. Using only the parameters given, make this equation dimensionless. Hint 1: first find a combination of ` and/or and/or A and/or T to make x, y, and t dimensionless.(It is clear that a different combination will be needed to make t dimensionless than that for x and y.) Hint 2: let c = q TA . What are the dimensions of c? (Note that c is known as the ìwave speed.î)A chromel-constantan type thermocouple has a cold junction (or cold terminal) at the temperature of 20ºC. The tables provide the following values for this thermocouple: 0°C for e.m.f = 0.000 mV; 20ºC for e.m.f = 1192 mV and 200ºC for e.m.f = 13419 mV. To determine:(a) The Seebeck coefficient (or proportionality constant) of this thermocouple. (b) The electrical voltage at the thermocouple terminals when the hot junction (or terminal hot) is at a temperature of 200ºC.A support beam used in one of the designs for the theme park, is subjected to vibrations along its length; emanating from two machines situated at opposite ends of the beam. The displacement caused by the vibrations can be modelled by the following equations: x_1=3.75 sin(100πt+2π/9) x_2=4.42 sin(100πt-2π/5) You are required to determine the followings for the vibration of this beam: i. State the amplitude, phase angle, frequency and periodic time of each of these waves. ii. When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement? iii. At what time does each vibration first reach a displacement of −2??? iv. Use the compound angle formulae to expand x_1 and x_2 into the form ? sin 100?? ± ? cos 100??, where ? and ? are numbers to be found. v. Using your answers from part iv, express x_1+x_2 in a similar form. Convert this expression into the equivalent form ? sin (100?? + α)