In a two-dimensional vortex flow, the fluid flows in circular paths around the center of the vortex. The magnitude of the velocity decreases with distance from the center. The stream function for a two-dimensional vortex centered at the origin is ψ=ln sqrt(x^2+y^2) where the x--y plane is horizontal and x and y are in meters. Show that continuity of the flow is satisfied and determine the magnitude of the horizontal velocity at A, where x=−0.2m, y=0.4m. Express your answer in m/s to three significant figures

10.8 What happens to an employee who passes through the socialization process?

10.7     What are the goals of a good induction program?

To increase load carrying capacity of a tube (ID: 40mm, OD: 45mm) it was determined in the last minute that it should be reinforced by combining it with a larger tube (ID: 45mm, OD: 50mm) through shrink fitting. Measurement after machining indicated the OD of the inner tube to be 45.012 mm and ID of the outer tube to be 44.950mm. A) Find the maximum torque the assembled tube can carry. B) After assembling, if the composite tube is subjected to a bending moment of 0.675 kN*m and a torque of 0.9 kN*m, find the factor of safety in both tubes using the ​Distortion Energy Theory. ​Assume S_​YT to be 415 MPa.

Discuss the effect of (i) grain size and (ii) phases amounts on the mechanical properties of the steel metal

An aircraft is in level flight at airspeed v(t) m/s with thrust T(t) N at cruising altitude. Suppose that at v0 = 250 m/s, the aerodynamic drag experienced by the aircraft at this altitude is:

Fd(v) = 0.25v 2 . (1)

Then, an extremely simplified model relating v(t) to T(t) is:

mv˙(t) + Fd(v(t)) = T(t), (2)

where m = 25000 kg. Assume v(t) is always positive.

Question 1. Linearize (2) at v0 = 250 m/s, and an appropriate nominal thrust T0. That is, create a new linear system model ˙δv + aδv = bδT that is accurate for small perturbations δv(t) = v(t) − v0, δT = T(t) − T0.

Question 2. Suppose we want the aircraft to fly at v0 = 250 m/s. However, precise modelling of drag is very difficult. Suppose in reality the dynamics are slightly different:

mv˙(t) + 0.23v(t) 2 = T(t). (3)

To control v(t) to be close to the reference 250m/s, you try using a proportional controller to control the thrust:

T(t) = T0 + k(v0 − v(t)), (4) with k = 100.

Here T0 is the value calculated in Question 1, but the controller is applied to the true dynamics (3). Find the final final value of v in: (a) open loop (i.e. just apply T(t) = T0), and (b) closed loop (using (4)). You may need to solve a quadratic equation. Recall that v(t) is assumed to be positive. Which one is better?

A 6 inch diameter water main in your town has become very rough due to rust and corrosion. It has been suggested that the flowrate through this pipe can be increased by inserting a smooth plastic liner into the pipe. Although the new diameter will be smaller, the pipe will be smoother. Will such a procedure produce a greater flowrate? List all assumptions and all calculations.

IMPORTANT NOTE: Please have the answer complete, CLEAR and computer generated!!

Air enters a 30-cm-diameter cooling section at 1 atm, 35 C, and 60 percent relative humidity at 120 m/min. The air is cooled by passing it over a cooling coil through which cold water flows. The water experiences a temperature rise of 8 C. The air leaves the cooling section saturated at 20 C.

(a) Determine the rate of heat transfer. Round your answer to the nearest tenth.

     Q_out = _____ kJ/min

(b) Determine the mass flow rate of the water. Round your answer to the nearest hundredth

     m_{cooling water} = _____ kg/min

(c) Determine the exit velocity of the airstream. Round your answer to the nearest ones place.

     V₂ = _____ m/min

Considering only conductive heat losses, calculate the heating load in BTU/H for a home constructed as follows:

walls: 2 inch hardwood planks, plus 1/2 inch lapped wood siding and 1/2 sheetrock (drywall) inside.

roof: flat, 1 inch plywood finished with asbestos shingles, with 3.5 inches fiberglass insulation.

floor: 25/32 inch wood subfloor with 3/4 inch hardwood finish, over unheated crawl space

windows: single pain glass, covering 25% of the wall area

House size is 28 ft x 40 ft x 10 ft high

Assume the home is maintained 40F warmer than outside, and 10F warmer than the crawlspace.

Assume your answer in units of BTU/hr

In a delivery line for carbontetrachloride at the constant flow rate of 4 X 10^(-5) m3/s, the first 1000 mm long section is of 20 mm inside diameter smooth pipe followed by another 1000 mm long section of 50 mm inside diameter smooth pipe as shown in the following figure. Estimate the pressure drop over the entire length of delivery line. Neglect the minor losses due to sudden enlargement of pipe diameter.

Data: For carbon tetrachloride, Viscosity = 10^(-3) Pa.sec and density = 1500 kg/m3 For laminar flow, consider fanning friction factor, f = 16/Re
For transitional-turbulent flow, f = 0.079Re^(-0.25)

Air is compressed adiabatically in a piston–cylinder assembly from 1 bar, 300 K to 4 bar, 600 K. The air can be modeled as an ideal gas and kinetic and potential energy effects are negligible. Determine the amount of entropy produced, in kJ/K per kg of air, for the compression. What is the minimum theoretical work input, in kJ per kg of air, for an adiabatic compression from the given initial state to a final pressure of 4 bar? Note that work is positive into the compressor.

A conduit carrying water vapor has one inlet and two exits. At the inlet, the velocity 25 m/s, the pressure is 4 bar and the temperature is 350 Celsius. The area at the inlet is 0.2 m^2 . At both the exits, the temperature and pressure are 300 Celsius and 3 bar respectively. The volumetric flow rate is identical at the two exits. Assuming steady-state conditions, calculate the volumetric flow rate at the exits.

Three phase voltage is spaced? is it 120 degrees apart?