HW4 EX1: An automobile moving over a rough road (Fig. 1.64) can be modeled considering (a) weight of the car body, passengens, seats, front wheels, and rear wheels; (b) elasticity of tires (suspension), main springs, and seats; and (c) damping of the seats, shock absorbers, and tires. Develop three mathematical models of the system using a gradual refinement in the modeling process.
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- The pressure rise, Ap across a centrifugal pump from a given manufacture can be expected to depend on the angular velocity of the impeller w, the Diameter D, of the impeller, the volume flow-rate Q, and the density of the fluid, p. By using the method of repeating variables show that Др ρω- D wD³ A model pump having an impeller diameter of 0.200 m is tested in the laboratory using water. The pressure rise when tested at an angular velocity of 407 rad/sec is shown on the graph. What would be the pressure rise for a geometrically similar pump with an impeller diameter of 0.30 m used to pump water operating at an angular velocity of 807 rad/sec and at a flow rate of 0.070 m³/s? Sol: 40 30 (kPa) Apm 10 0 € 0.02 Q Model data (₁ = 40 rad/s Dm = 20 cm 0.04 0.06 Qm (cubic meters per sec) 0.08QI:Capillary rise for distilled water is (h) inside the tube is varies with the diameter of the tube (d) density of the fluid (p), gravity (g),the angle of contact (8), and surfaces tension (6).Using Buckingham's theorem to find a functional relation for (h) with other parameters.3. Find the two-dimensional temperature distribution T(r,z) under steady state condition. Where, To=20 °C, TL=5200 °C. The density, conductivity and specific heat of the material are p 800 kg/m³, k=200 W/m.K, and cp=2500 J/kg.K, respectively. Also, r= 520 cm and L=1040cm. To TL L To
- Q2 Consider a conical receiver shown in Figure 2. The inlet and outlet liquid volumetric flow rates are Fl and F2, respectiveily. ccorresponding radius in r) Figure 2 Conicul tank Develop the model equation with necessary assumption(s) with respect to the liquid height h. ii. What type of mathematical model is this? 1 R %3D Hint: Model: = F, – Fz, where the volume V=r h=nh, since = substitute V and Fz expressions and get the final form. %3D %3D %3D dt H.In the Fig. 2 below, let Ki = K2 = K and ti = t=t. %3D T -T X Fig. 2 (a) Let T= 0 °C and T= 200 °C. Solve for T: and unknown rates of heat flow in term of k and t. MEC_AMO_TEM_035_02 Page 2 of 11 Finite Element Analysis (MECH 0016.1) – Spring - 2021 -Assignment 2-QP (b) Let T- 400 °C and let fs have the prescribed value f. What are the unknowns? Solve for them in term of K, t, and f.The governing equation of motion for a base motion system is given by (assume the units are Newton) mä(t)+ci(t)+kx(t) =cY@, cos(@,t) +kY sin(@t) %3D Given that m = 180 kg, c = 30 kg/s, Y = 0.02 m, and о, — 3.5 rad/s %3| 1. Use Excel or Matlab to find the largest value of the stiffness, k that makes the transmissibility ratio less than 0.85 2. Using the value of the stiffness obtained in part (1), determine the transmitted force to the base motion system using Matlab or Excel. 3. Display and discuss your results.
- This problem is (16.23) from a book "Thermodynamics and Statistical Mechanics An Integrated Approach by M. Scott Shell"is a mass hanging by a spring under the influence of gravity. The force due to gravity, Fg, is acting in the negative-y direction. The dynamic variable is y. On the left, the system is shown without spring deflection. On the right, at the beginning of an experiment, the mass is pushed upward (positive-y direction) by an amount y₁. The gravitational constant g, is 9.81 m/s². DO C.D Frontly у Your tasks: No Deflection m k Fg = mg Initial Condition y m k Write down an expression for the total energy If as the sum Write down an expression for the total energy H Fg = mg Figure 3: System schematic for Problem 4. Yi & X Write down, in terms of the variables given, the total potential energy stored in the system when it is held in the initial condition, relative to the system with no deflection. as the sum of potential and kinetic energy in terms of y, y, yi C After the system is released, it will start to move. Write down an expression for the kinetic energy of the system, T, in terms of…62. •A 5-kg object is constrained to move along a straight line. Its initial speed is 12 m/s in one direction, and its final speed is 8 m/s in the opposite Complete the graph of force versus time with direction. F (N) (s) appropriate values for both variables (Figure 7-26). Several answers are correct, just be sure that your answer is internally consistent. Figure 7-26 Problem 62
- Surface tension is due to uneven molecular attraction between immiscible fluid media and solid surface. Its importance is governed by dimensionless parameter Which of the Inertia force called Weber number given by We = Surface tension force™ following statements are correct? (i) Surface tension becomes important when the length scale L is small such as in ink jet printing, coating of thin film, oxygenation of water by falling rain drops. (ii) 111 Super-hydrophobicity can be achieved by micro/nano texturing of surface such as in lotus leave, butterfly and dragonfly wing. During oil spill in ocean, oil floats and spreads out due to gravity. By conservation of mass, the oil film becomes thinner as it spreads. Finally, the surface tension force becomes important causing the formation of tiny oil droplets. (A) (B) (C) (D) (i) and (ii) (i) and (iii) (ii) and (iii) All of the aboveA lunar excursion module (LEM) weighs 1500 kg; on earth where g=9.75 mps2. Calculate: Match each item to a choice: its weight in kgf on the surface of the moon where q = 1.80 mps? the force required in pounds (Ib), to accelerate the module at 33 fps2 Choices: : 15087 : 15087 : 3410.53 : 261.5 : 3617.23 : 1538.5 : 183.21 i none of these : 246.15Let's assume that the outdoor temperature in your region was 1 C on 26.12.2002. Let's assume that you use a 2088 W heater in the room in order to keep the indoor temperature of the room at 20 ° C. In the meantime, a 68 W light bulb for lighting, a computer you use to solve this question and load it into the system (let's assume it consumes 217 W of energy), you and your two friends (three people in total) are in the room to assist you in solving the questions. A person radiates 45 J of heat per second to his environment. When you consider all these conditions, calculate the exergy destruction caused by the heat loss from the exterior wall of your room.