Help explain plot and how to determine last two iterations. A pump is being installed to circulate water through a piping system in an industrial plant. The operating point of the system, meaning the fluid flow rate, pressure increase across the pump, and the power consumed by the pump, is to be determined. The equations for the two components are:- **Pump Pressure:** \[ P = 1000 - 56 \cdot Q^{1.6} \]- **Piping Network Pressure Drop:** \[ P = 50 \cdot Q + 115 \cdot Q^2 \]where \( Q \) is the flow rate in m\(^3\)/s and \( P \) is the pressure drop in kPa.**Task:**a) Use successive substitution to solve for the operating point, choosing as trial values \( P = 200 \, \text{kPa} \) and \( Q = 1 \, \text{m}^3/\text{s} \). Consider the use of relaxation if necessary. Show the results of your first 5 iterations and last two iterations in a table along with the guess values at those iterations. Provide the operating flow, pressure across the pump, and power consumption by the pump (assume pump is 100% efficient). Plot the pump curve and system curve for the pipe network and discuss how the solution relates to the curves.

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A pump is being installed to circulate water through a piping system in an industrial plant. The operating point of the system, meaning the fluid flow rate, pressure increase across the pump, and the power consumed by the pump, is to be determined. The equations for the two components are: Pump Pressure: Piping Network Pressure Drop: P = 1000-56-Q1.6 P = 50.Q+ 115-Q² where Q is the flow rate in m³/s and P is the pressure drop in kPa. a) Use successive substitution to solve for the operating point, choosing as trial values P = 200 kPa and Q = 1 m³/s. Consider the use of relaxation if necessary. Show the results of your first 5 iterations and last two iterations in a table along with the guess values at those iterations. Provide the operating flow, pressure across the pump, and power consumption by the pump (assume pump is 100% efficient). Plot the pump curve and system curve for the pipe network and discuss how the solution relates to the curves.

A pump is being installed to circulate water through a piping system in an industrial plant. The operating point of the system, meaning the fluid flow rate, pressure increase across the pump, and the power consumed by the pump, is to be determined. The equations for the two components are: Pump Pressure: Piping Network Pressure Drop: P = 1000-56-Q1.6 P = 50.Q+ 115-Q² where Q is the flow rate in m³/s and P is the pressure drop in kPa. a) Use successive substitution to solve for the operating point, choosing as trial values P = 200 kPa and Q = 1 m³/s. Consider the use of relaxation if necessary. Show the results of your first 5 iterations and last two iterations in a table along with the guess values at those iterations. Provide the operating flow, pressure across the pump, and power consumption by the pump (assume pump is 100% efficient). Plot the pump curve and system curve for the pipe network and discuss how the solution relates to the curves.

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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Help explain plot and how to determine last two iterations.

A pump is being installed to circulate water through a piping system in an industrial plant. The operating point of the system, meaning the fluid flow rate, pressure increase across the pump, and the power consumed by the pump, is to be determined. The equations for the two components are:

- **Pump Pressure:**
\[ P = 1000 - 56 \cdot Q^{1.6} \]

- **Piping Network Pressure Drop:**
\[ P = 50 \cdot Q + 115 \cdot Q^2 \]

where \( Q \) is the flow rate in m\(^3\)/s and \( P \) is the pressure drop in kPa.

**Task:**

a) Use successive substitution to solve for the operating point, choosing as trial values \( P = 200 \, \text{kPa} \) and \( Q = 1 \, \text{m}^3/\text{s} \). Consider the use of relaxation if necessary. Show the results of your first 5 iterations and last two iterations in a table along with the guess values at those iterations. Provide the operating flow, pressure across the pump, and power consumption by the pump (assume pump is 100% efficient). Plot the pump curve and system curve for the pipe network and discuss how the solution relates to the curves.

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