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. b) The pip material can handle pressures of up to 150 psi prior to rupture. Discuss whether or not the system specified above is a workable solution. If it is not, indicate how either the pump or pipes could be modified to make the solution workable. If it is workable, indicate how changes in the pump or pipes would result in a non-workable solution.
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. b) The pip material can handle pressures of up to 150 psi prior to rupture. Discuss whether or not the system specified above is a workable solution. If it is not, indicate how either the pump or pipes could be modified to make the solution workable. If it is workable, indicate how changes in the pump or pipes would result in a non-workable solution.
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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![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 m³/s and \( P \) is the pressure drop in kPa.
**Tasks:**
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.
b) The pipe material can handle pressures of up to 150 psi prior to rupture. Discuss whether or not the system specified above is a workable solution. If it is not, indicate how either the pump or pipes could be modified to make the solution workable. If it is workable, indicate how changes in the pump or pipes would result in a non-workable solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff0e69105-edad-4e40-a986-7d2af8f1b9bd%2F6bd720bc-e309-4852-b6cf-d682bb8b8e84%2F9lkq06w_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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 m³/s and \( P \) is the pressure drop in kPa.
**Tasks:**
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.
b) The pipe material can handle pressures of up to 150 psi prior to rupture. Discuss whether or not the system specified above is a workable solution. If it is not, indicate how either the pump or pipes could be modified to make the solution workable. If it is workable, indicate how changes in the pump or pipes would result in a non-workable solution.
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