b The figure shows the cross section of a channel carrying water. Determine h, b and that minimize the length of the wetted perimeter while maintaining a cross- sectional area of 8 m². (Minimizing the wetted perimeter results in least resistance to the flow.) Ans: 14- Given. A = 8m² To Find: ktb h A Determine, h, b, 0 of wetted perimeter. h tano = m that minimize the length
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- An aluminum wire having a cross-sectional area equal to 4.60 x 10-6 m? carries a current of 7.50 A. The density of aluminum is 2.70 g/cm³. Assume each aluminum atom supplies one conduction electron per atom. Find the drift speed of the electrons in the wire. 1.95E-4 The equation for the drift velocity includes the number of charge carriers per volume, which in this case is equal to the number of atoms per volume. How do you calculate that if you know the density and the atomic weight of aluminum? mm/s2. Heat conduction in a square plate Three sides of a rectangular plate (@ = 5 m, b = 4 m) are kept at a temperature of 0 C and one side is kept at a temperature C, as shown in the figure. Determine and plot the ; temperature distribution T(x, y) in the plate. The temperature distribution, T(x, y) in the plate can be determined by solving the two-dimensional heat equation. For the given boundary conditions T(x, y) can be expressed analytically by a Fourier series (Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 1993):A reservoir discharging water through sluices at a depth hbelow the water surface area Afor various values has given below: hft1011121314( . .)Asqft9501070120013501530If tdenotes time in minutes, the rate of fall of the surface is given by 48dhhAdtEstimate the time taken for the water level to fall from 14 to 10 ft. above the sluices.
- Suppose we have an 80-lb lead-acid battery. 10% of the weight of the battery is active material on the plates, i.e., we have a total of 8 lb of active Pb and PbO, on the plates that can be used to make electric power. Use the Gibbs free energy method to estimate the total stored energy in the battery. Assume that the open circuit voltage for a lead-acid cell is 2.1 V. [The answer should be a little less than 1 kilowatt-hour of energy.]Q.4 In an experimental setup, mineral oil is filled in between the narrow gap of two horizontal smooth plates. The setup has arrangements to maintain the plates at desired uniform temperatures. At these temperatures, ONLY the radiative heat flux is negligible. The thermal conductivity of the oil does not vary perceptibly in this temperature range. Consider four experiments at steady state under different experimental conditions, as shown in the figure Q1. The figure shows plate temperatures and the heat fluxes in the vertical direction. What is the steady state heat flux (in W m) with the top plate at 90°C and the bottom plate at 45°C? [4] 30°C 70°C 40°C 90°C flux = 39 Wm-2 flux =30 Wm2 flux = 52 Wm 2 flux ? Wm-2 60°C 35°C 80°C 45°C Experiment 1 Experiment 2 Experiment 3 Experiment 44. The outer facing of a room is constructed from 0.75 m thick brick, 25 cm of mortar, 12 cm of limestone (k=0.186 W/mK) and 0.5 m of plaster (0.096 W/mK). Thermal conductivities of mortar and brick are both 0.52 W/mK. Assume that the heat transfer coefficients on the inside (plaster side) and outside (brick side) surfaces of the wall to be 8 and 24 W/(m^2 K), respectively. Calculate the overall coefficient of heat transfer (W/(m^2 K). Show your solution
- The following is used to model a wave that impacts a concrete wall created by the US Navy speed boat.1. Derive the complete piecewise function of F(t) and F()The concrete wall is 2.8 m long with a cross-section area of 0.05 m2. The force at time equal zero is 200 N. It is also known that the mass is modeled as lumped at the end of 1200 kg and Young’s modulus of 3.6 GPa2. Use *Matlab to simulate and plot the total response of the system at zero initial conditions and t0 = 0.5 sElectromagnetic Pulse propagating at oblique angle to a dielectric interface Consider a gaussian wave pulse propagating along the z-axis from region 1 with refractive index n1 and onto a dielectric interface y = m z (for all x). To the left of this dielectric interface, the refractive index is n2. Devise an initial value computer algorithm to determine the time evolution of the reflected and transmitted electromagnetic fields for this pulse. e.g., n1 = 1 , n2 = 2 initial profile (t = 0, with z0 < 0) Ex = E0 exp[-a (z-z0)^2] By = n1 * Ex Choose parameters so that the pulse width is at least a fact of 8 less than the z- domain of integration ( -L < z < L). For the slope of the interface, one could choose m = 1.SITUATION 1 (Fluid Flow in a Closed Conduit) Consider a fluid, with density (p) of 998.21 kg/m³ and dynamic viscosity (u) of 1.002 x 103 N-s/m², flowing in a 2000-meter long, 50-mm diameter smooth round pipe with velocity of 2.5 m/s. The energy loss on the pipe flow (he) due to friction between the pipe and the fluid is determined using Darcy-Weisbach equation, given as h₁ = f (²) (1/1) where f is the friction factor, L is the length of the pipe, D is the diameter of the pipe, V is the velocity of the flow, and g is the gravitational acceleration. The friction factor may be determined using an empirical equation developed by Nikuradse for flow in smooth pipes, given as 1 =0.869 In (Re√7)-0.8 where Re is the Reynolds number of the flow, determined as VDp R₂ = μl The friction factor equation given is only valid for flows with Reynolds number higher than 4000 (turbulent flow). Guide Questions: Determine the Reynolds number of the flow. Is the Nikuradse equation for friction factor…
- A bicycle wheel has a diameter of 64.6 cm and a mass of 1.87 kg. Assume that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is placed on a stationary stand and a resistive force of 125 N is applied tangent to the rim of the tire. (a) What force must be applied by a chain passing over a 8.96 cm diameter sprocket if the wheel is to attain an acceleration of 4.49 rad/s22? (b) What force is required if the chain shifts to a 5.57 cm diameter sprocket?The density of a sample of FCC palladium is 11.98 g/cm3, and its lattice parameter is 3.8902 A...Calculate (a) the fraction of the lattice points that contain vacancies: and (b) the total number of vacancies in a cubic centimeter of Pd.A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution with 1/5 pound of salt per gallon is added to the tank at 10 gal/min, and the resulting mixture is drained out at 5 gal/min. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t) which is valid up until the point at which the tank overflows. Q' (t) = = (b) Find the quantity of salt in the tank as it's about to overflow. esc C ✓ % 1 1 a 2 W S # 3 e d $ 4 f 5 rt 99 6 y & 7 h O u * 00 8 O 1 9 1 O