**Problem Statement:**Water flows horizontally in a pipe of diameter 9.1 cm at a rate of 0.745 m/s and a gauge pressure of \(7.76 \times 10^3\) Pa. The fluid (still in the pipe) then descends a 3.41 m high hill, passes through a reducer and into a smaller 3.55 cm diameter pipe, and then flows horizontally again. Determine the gauge pressure (in Pa) in the lower section of pipe.---**Explanation:**This problem involves fluid dynamics principles, particularly Bernoulli’s equation and the continuity equation. The analysis starts with water moving through a pipe, undergoing a change in elevation, and subsequently flowing through a section of different diameter. To find the gauge pressure in the lower section, the changes in velocity and pressure due to the pipe's diameter reduction and hill descent need to be calculated.Key concepts:1. **Continuity Equation**: This ensures mass conservation, where the product of cross-sectional area and velocity remains constant across different sections of the pipe.2. **Bernoulli’s Equation**: This relates pressure, velocity, and height in a flowing fluid, accounting for the conservation of energy.**Note:** - It’s essential to convert all units consistently, using meters for length and Pascal for pressure.- The density of water and gravitational acceleration may be needed for calculations.

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Water flows horizontally in a pipe of diameter 9.1 cm at a rate of 0.745 m/s and a gauge pressure of 7.76x10^3 Pa. The fluid (still in the pipe) then descends a 3.41 m high hill, passes through a reducer and into a smaller 3.55 cm diameter pipe, and then flows horizontally again. Determine the gauge pressure (in Pa) in the lower section of pipe.

Water flows horizontally in a pipe of diameter 9.1 cm at a rate of 0.745 m/s and a gauge pressure of 7.76x10^3 Pa. The fluid (still in the pipe) then descends a 3.41 m high hill, passes through a reducer and into a smaller 3.55 cm diameter pipe, and then flows horizontally again. Determine the gauge pressure (in Pa) in the lower section of pipe.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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