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Ola Williams

Ola W.

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A roast turkey is taken from an oven when its temperature has reached $ 185^{\circ}F $ and is placed on a table in a room where the temperature is $ 75^{\circ}F $. The graph shows how the temperature of the turkey decreases and eventually approaches room temperature. By measuring the slope of the tangent, estimate the rate of change of the temperature after an hour.

A roast turkey is taken from an oven when its temperature has reached $ 185^{\circ}F $ and is placed on a table in a room where the temperature is $ 75^{\circ}F $. The graph shows how the temperature of the turkey decreases and eventually approaches room temperature. By measuring the slope of the tangent, estimate the rate of change of the temperature after an hour.

Calculus: Early Transcendentals

Limits and Derivatives

Derivatives and Rates of Change

Questions asked

INSTANT ANSWER

Calculate the wave speed and wavelength for deep water, intermediate water and shallow water having a common wave frequency of 0.125Hz and at water depth intervals of 1m, 3m, 5m, 10m and 15m. Plot the profiles for the calculated intermediate and shallow water depth criterion.

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INSTANT ANSWER

The management of physical assets (selection, maintenance, inspection and renewal) plays a key role in determining the operational performance and profitability of industries that operate assets as part of their core organisation. It represents a cross disciplinary collaboration to achieve best net, sustained value for money in the selection, design, acquisition, operations, maintenance and renewal or disposal of physical infrastructure and equipment. Given these requirements provide one of the three outlined definitions of asset management.

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Celine Ibrahim verified

Numerade educator

A DFIG wind turbine has six-pole, 60 Hz three-phase, Y-connected induction generator. The terminal voltage of the generator is 690 V. The effective turns ratio of the generator is 2. The rotor parameters of the machine are as follows: Rs = Rr = 5 mΩ. Xls = Xlr = 150 mΩ and Xm = 5 Ω . Assuming the stator voltage is the reference phasor, the injected voltage seen from the stator side is adjusted to V ′ = 5∠−120°V by a PWM technique. Compute the developed power, developed torque, rotor injected power, and stator power at 1230 rpm.

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ANSWERED

Celine Ibrahim verified

Numerade educator

A type 2 wind turbine has a four-pole, 50 Hz three-phase, Y-connected induction generator. The terminal voltage of the generator is 690 V. The parameters of the machine are Rr = 15 mΩ Xlr = 180 mΩ; and Xm = 8 Ω. Assume the impedance of the stator circuit is much smaller than the impedance of the magnetizing branch. Compute the pull-out power. Repeat the solution after inserting a 0.01Ω resistance in the rotor circuit as referred to the stator. The duty ratio of its solid-state switching circuit is 50%.

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ANSWERED

Celine Ibrahim verified

Numerade educator

A type 1 wind turbine with a six-pole, 60 Hz three-phase, Y-connected induction generator is spinning at 1250 rpm. The terminal voltage of the generator is 690 V. the parameters of the machine are: Rs = Rr 10 mΩ, Xls = Xlr = 100 mΩ and Xm = 2Ω. Compute the stator current.

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ANSWERED

Narayan Hari verified

Numerade educator

A horizontal axis wind turbine operating at sea level has a blade diameter of 40 m. Find the maximum amount of power that the turbine can extract from the wind for wind speeds of 2 m/s and 8 m/s

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ANSWERED

Narayan Hari verified

Numerade educator

A wind turbine has a rotor diameter of 33 m. At a wind speed of 13 m/s, a) What is the power in the wind? b) What is the power in the shaft of the turbine if the rotor has a power coefficient of 0.35? c) If the speed of rotation of the shaft is 35 r.p.m. calculate the tip speed and torque on the shaft.

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INSTANT ANSWER

Sketch and explain the Cp/TSR curve of a wind turbine rotor. Define Cp and TSR. What is the Betz limit.

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INSTANT ANSWER

Consider a 700 kW, 45 m diameter horizontal axis, fixed speed wind turbine operating in a wind speed of 12 m/s. The three blades drive a generator through a three-stage gearbox of overall ration 1:50. The induction generator is connected directly to the 50 Hz grid and keeps the high-speed shaft at 1500 rpm and hence the low-speed shaft rotates at 30 rpm. Calculate the Cp, the TSR and the torque on the shafts.

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Nicholas Mogoi verified

Numerade educator

Calculate the kinetic energy passing through a 10 m2 area for 10 hours if the wind speed is (a) 4 m/s and (b) 8m/s, assuming the air density is 1.23 kg/m3. Determine the power in the wind in both cases.

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