**Problem 7-67: Dimensional Analysis of Fluid Flow in a Pump**A liquid with density \( \rho \) and viscosity \( \mu \) is pumped at a volume flow rate \( \nu \) through a pump with a diameter \( D \). The blades of the pump rotate at an angular velocity \( \omega \). The pump provides a pressure increase \( \Delta P \) to the liquid. **Task:** Using dimensional analysis, derive a dimensionless equation for \( \Delta P \) as a function of the other parameters in the scenario. Identify any established non-dimensional parameters in your result.**Hint:** For consistency, it is recommended to select a length, a density, and a velocity (or angular velocity) as repeating variables.

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7–67 A liquid of density p and viscosity µ is pumped at volume flow rate b through a pump of diameter D. The blades of the pump rotate at angular velocity a.' pump supplies a pressure rise AP to the liquid. Using dimensional analysis, generate a dimensionless relationship for AP as a function of the other parameters in the problem. Identify any established nondimensional parameters that appear in your result. Hint: For consistency (and whenever possible), it is wise to choose a length, a density, and a velocity (or angular velocity) as repeating variables.

7–67 A liquid of density p and viscosity µ is pumped at volume flow rate b through a pump of diameter D. The blades of the pump rotate at angular velocity a.' pump supplies a pressure rise AP to the liquid. Using dimensional analysis, generate a dimensionless relationship for AP as a function of the other parameters in the problem. Identify any established nondimensional parameters that appear in your result. Hint: For consistency (and whenever possible), it is wise to choose a length, a density, and a velocity (or angular velocity) as repeating variables.

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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Question

**Problem 7-67: Dimensional Analysis of Fluid Flow in a Pump**

A liquid with density \( \rho \) and viscosity \( \mu \) is pumped at a volume flow rate \( \nu \) through a pump with a diameter \( D \). The blades of the pump rotate at an angular velocity \( \omega \). The pump provides a pressure increase \( \Delta P \) to the liquid.

**Task:**

Using dimensional analysis, derive a dimensionless equation for \( \Delta P \) as a function of the other parameters in the scenario. Identify any established non-dimensional parameters in your result.

**Hint:** For consistency, it is recommended to select a length, a density, and a velocity (or angular velocity) as repeating variables.

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