Answer all questions below showing revelent calculations and working with explanation where necessary.1.Create a mathematical model for the system shown.2.Develop a transfer function for 0(s)/Qi(s), state the constants that you have used in your transfer function. [Hint: You would also need to derive Q(s)/Qi(s) to predict a theoretical value for the increase in rotational speed ] [Note: Omega, Q=Angular speed]3. With the use of theoretical values, determine the theoretical increase in rotational speed expected for the water wheel when the inflow is increased by a step. This should be repeated for three different step input values. Show calculations and working throughout. Water Wheel DesignYou have been asked to design a water wheel that will generate electricity from a river in thenorthern range. Because the flow rate from the river can fluctuate depending on seasonalrainfall, you have decided to include a holding tank that will maintain a fairly constant water leveWater from this tank will then fall onto the wheel to generate the electricity. Because there willstill be fluctuations due to the flow rate of the river, the final device will need to includeautomatically controlled valving to maintain a constant power output.Because this is a very complex system, you have decided to develop a simplified mathematicalmodel for the system, to help you firstly predict how changes to the in-flow rate of the streamwill affect the rotational speed of the water wheel. A simple representation of this system isshown below.REleWater wheelAnswer all questions below showing revelent calculations and working with explanation wherenecessary.1.Create a mathematical model for the system shown.2.Develop a transfer function for 8(s)/Qi(s), state the constants that you have used in yourtransfer function. [Hint: You would also need to derive Q(s)/Qi(s) to predict a theoretical valuefor the increase in rotational speed ] [Note: Omega, Q=Angular speed]3. With the use of theoretical values, determine the theoretical increase in rotational speedexpected for the water wheel when the inflow is increased by a step. This should be repeatedfor three different step input values. Show calculations and working throughout.

To find:Mathematical modelTransfer functionStep response

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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Answer all questions below showing revelent calculations and working with explanation where necessary.

1.Create a mathematical model for the system shown.

2.Develop a transfer function for 0(s)/Qi(s), state the constants that you have used in your transfer function. [Hint: You would also need to derive Q(s)/Qi(s) to predict a theoretical value for the increase in rotational speed ] [Note: Omega, Q=Angular speed]

3. With the use of theoretical values, determine the theoretical increase in rotational speed expected for the water wheel when the inflow is increased by a step. This should be repeated for three different step input values. Show calculations and working throughout.

Water Wheel Design
You have been asked to design a water wheel that will generate electricity from a river in the
northern range. Because the flow rate from the river can fluctuate depending on seasonal
rainfall, you have decided to include a holding tank that will maintain a fairly constant water leve
Water from this tank will then fall onto the wheel to generate the electricity. Because there will
still be fluctuations due to the flow rate of the river, the final device will need to include
automatically controlled valving to maintain a constant power output.
Because this is a very complex system, you have decided to develop a simplified mathematical
model for the system, to help you firstly predict how changes to the in-flow rate of the stream
will affect the rotational speed of the water wheel. A simple representation of this system is
shown below.
R
Ele
Water wheel
Answer all questions below showing revelent calculations and working with explanation where
necessary.
1.Create a mathematical model for the system shown.
2.Develop a transfer function for 8(s)/Qi(s), state the constants that you have used in your
transfer function. [Hint: You would also need to derive Q(s)/Qi(s) to predict a theoretical value
for the increase in rotational speed ] [Note: Omega, Q=Angular speed]
3. With the use of theoretical values, determine the theoretical increase in rotational speed
expected for the water wheel when the inflow is increased by a step. This should be repeated
for three different step input values. Show calculations and working throughout.

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