### Fluid Dynamics Problem: Calculating Fluid Speed in a Tapered Pipe System**Problem Statement:**An incompressible ideal fluid flows steadily through a pipe. At one point in the pipe, the fluid passes through a reducer into a smaller pipe. The fluid speed at a point where the pipe diameter is 6.95 cm is 1.95 m/s. What is the speed of the fluid at a point where the pipe has narrowed to a diameter of 3.75 cm?**Concepts Covered:**This problem involves applying the principle of conservation of mass in fluid dynamics, specifically using the equation of continuity for incompressible flow. According to the equation of continuity, the mass flow rate must remain constant in a streamline flow of an ideal fluid.**Equation:**\[ A_1 \cdot v_1 = A_2 \cdot v_2 \]Where:- \( A_1 \) is the cross-sectional area at the wider pipe section.- \( v_1 \) is the fluid speed at the wider section (1.95 m/s).- \( A_2 \) is the cross-sectional area at the narrower pipe section.- \( v_2 \) is the fluid speed at the narrower section, which needs to be calculated.**Steps:**1. Calculate the cross-sectional areas \( A_1 \) and \( A_2 \). - \( A = \pi \left(\frac{d}{2}\right)^2 \)2. Use the equation of continuity to solve for \( v_2 \).This exercise helps demonstrate fluid dynamics principles in practical scenarios involving piping systems.

Given data: The pipe diameter at one point (d1) = 6.95 cm Speed (v1) = 1.95 m/s The diameter of…

An incompressible ideal fluid flows steadily through a pipe. At one point in the pipe, the fluid passes through a reducer into a smaller pipe. The fluid speed at a point where the pipe diameter is 6.95 cm is 1.95 m/s. What is the speed of the fluid at a point where the pipe has narrowed to a diameter of 3.75 cm?

An incompressible ideal fluid flows steadily through a pipe. At one point in the pipe, the fluid passes through a reducer into a smaller pipe. The fluid speed at a point where the pipe diameter is 6.95 cm is 1.95 m/s. What is the speed of the fluid at a point where the pipe has narrowed to a diameter of 3.75 cm?

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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