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A well-designed drill bit minimizes the risk of burning your fingers when you remove the bit from the drill. To achieve that goal, an important design objective is to minimize the heat flow along its length while simultaneously making sure the drill bit doesn’t mechanically fail during operation. Assume the maximum temperature generated at the drill bit tip is attained quickly and remains constant so that the temperature gradient, Δ𝑇, along the shaft is constant with time. The length, L, of the shaft is fixed but its radius, R, is variable.

a.Derive the material index for this application. Assume the heat, q, flow is:

𝑞=(𝜆Δ𝑇𝜋𝑅^2)/𝐿 where 𝜆 is the thermal conductivity,and the failure torque is:𝑇f=(𝜋𝑅^3𝜎y)/4 Start the problem by listing the objective, constraints and free variables


When a pressure vessel has to be mobile its weight becomes important. Aircraft bodies, rocket casings and liquid natural gas containers are examples; they must be light, and at the same time, they must be safe. Therefore, the design of these vessels involves multiple constraints with a single objective.Let us assume you are involved in the selection of materials for the construction of such a pressure vessel. For simplicity, assume that the vessel is spherical and that the radius, R, and the pressure difference,P,across the wall are both fixed by design. Note that the volume of a thin-walled sphere is 4π(R^2)t. During operation, the pressure vessel should not yield,i.e.,the stress in the wall should not exceed 𝜎y. Assume the hoop stress in the wall is (PR)/(2t), where t is the thickness.


A) Derive the materials index, M1, for the design criteria. Start this problem by listing the objective, the constraints and the free variables.


https://imgur.com/a/44Txx5p


By using the following data only,evaluate pH2S/pH2 in equilibrium with Ag and a maHe conting 90 mol% Ag2s at 600c .Assume the gases are ideal and enthalpies are independent of temprature

4Ag(s)+S2(g)___ 2Ag2S(s) G873°=30,750 cal


H2(g) S2 H2S cal/k.mol

S298° 31.21 54.4 49.1


Hf298° 0 31,000 4800 cal/mol


6) A cubic crystal with a=5.60Å is set initially with the incident beam travelling along the [100] direction. The crystal is then rotated clockwise about [001] through an angle ω until the (460) reflection is first produced with Cu Kα radiation. Calculate the Bragg angle θ for the (460) reflection and determine the angle ω


6) A cubic crystal with a=5.60Å is set initially with the incident beam travelling along the [100] direction. The crystal is then rotated clockwise about [001] through an angle ω until the (460) reflection is first produced with Cu Kα radiation. Calculate the Bragg angle θ for the (460) reflection and determine the angle ω


6) A cubic crystal with a=5.60Å is set initially with the incident beam travelling along the [100] direction. The crystal is then rotated clockwise about [001] through an angle ω until the (460) reflection is first produced with Cu Kα radiation. Calculate the Bragg angle θ for the (460) reflection and determine the angle ω


Two impedances Z1 and Z2 are connected in parallel. The first branch takes a leading current of 16 A and has a resistance of 5 Ω, while the second branch takes a lagging current at 0.8pf. The applied voltage is 100+j200 V and the total power is 5 kW. Find branch impedances, total circuit impedance, branch currents and total circuit current.


If the currents in the three parallel branches of an ac circuit are given as I1 = 2530A, I2 = 25e-jΠ/6A and I3 = (50 + j 50)A, express the total current in the form (i) I Φ and (ii) Im sin (ωt + Φ).


Explain the conventional colouring and hatching that represents different materials


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