---
title: "A pump draws water of density \\(\\rho\\) from a large open reservoir, where the water is initially at rest, and delivers it at a constant volume flow rate \\(Q\\) through a pipe of uniform cross-sectional area \\(A\\). The water is discharged into the atmosphere at an exit located a vertical distance \\(h\\) above the reservoir surface. Assuming energy losses due to friction are negligible, which of the following expressions represents the minimum power delivered by the pump to the water?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/120646/"
date_modified: "2026-08-23T04:42:28+00:00"
---

# A pump draws water of density \(\rho\) from a large open reservoir, where the water is initially at rest, and delivers it at a constant volume flow rate \(Q\) through a pipe of uniform cross-sectional area \(A\). The water is discharged into the atmosphere at an exit located a vertical distance \(h\) above the reservoir surface. Assuming energy losses due to friction are negligible, which of the following expressions represents the minimum power delivered by the pump to the water?

A pump draws water of density \(\rho\) from a large open reservoir, where the water is initially at rest, and delivers it at a constant volume flow rate \(Q\) through a pipe of uniform cross-sectional area \(A\). The water is discharged into the atmosphere at an exit located a vertical distance \(h\) above the reservoir surface. Assuming energy losses due to friction are negligible, which of the following expressions represents the minimum power delivered by the pump to the water?

![A grayscale schematic of a fluid system. At the bottom, a wide open rectangular reservoir of liquid is shown with a flat horizontal surface. A single vertical pipe of uniform diameter and cross-sectional area \(A\) extends from beneath the reservoir surface up to a vertical height \(h\) above the surface, where it terminates in an open horizontal discharge spout pointing to the right. A small inline rectangular box on the vertical pipe near the base is labeled "Pump". A vertical double-ended dimension arrow extends from the level of the reservoir surface to the center of the discharge spout, labeled \(h\). A short arrow pointing right at the discharge nozzle is labeled with volume flow rate \(Q\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460148-nERLse.jpg)

- **A.** \(\rho Q g h + \dfrac{\rho Q^3}{2A^2}\)
- **B.** \(\rho Q g h + \dfrac{\rho Q^3}{A^2}\)
- **C.** \(\rho Q g h\)
- **D.** \(\dfrac{1}{2}\rho Q g h + \dfrac{\rho Q^3}{2A^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120646/*