Question

Water is flowing in a pipe with a varying cross-sectional area, and at all points the water completely fills the pipe. At area, $1,$ the cross-sectional area of the pipe is 0.070 $\mathrm{m}^{2}$ and the magnitude of the fluid velocity is 3.50 $\mathrm{m} / \mathrm{s} .$ What is the fluid speed at points in the pipe where the cross-sectional area is $(a) 0.105 \mathrm{m}^{2},$ (b) 0.047 $\mathrm{m}^{2}$ ?

Name: Problem 43, Chapter 13: College Physics
Uploaded: 2020-05-15T00:32:27-08:00
Duration: 2 min 38 s
Channel: Nathan Silvano
Description: Water is flowing in a pipe with a varying cross-sectional area, and at all points the water completely fills the pipe. At area, 1, the cross-sectional area of the pipe is 0.070 m^2 and the magnitude of the fluid velocity is 3.50 m / s . What is the fluid speed at points in the pipe where the cross-sectional area is (a) 0.105 m^2, (b) 0.047 m^2 ?

   Water is flowing in a pipe with a varying cross-sectional area, and at all points the water completely fills the pipe. At area, $1,$ the cross-sectional area of the pipe is 0.070 $\mathrm{m}^{2}$ and the magnitude of the fluid velocity is 3.50 $\mathrm{m} / \mathrm{s} .$ What is the fluid speed at points in the pipe where the cross-sectional
area is $(a) 0.105 \mathrm{m}^{2},$ (b) 0.047 $\mathrm{m}^{2}$ ?

College Physics

Hugh D. Young 9th Edition

Chapter 13, Problem 43

Instant Answer

Solved by Expert Nathan Silvano

05/15/2020

Step 1

This is given by the equation: \[v_1 \cdot A_1 = v_2 \cdot A_2\] where $v_1$ and $A_1$ are the initial speed and cross-sectional area of the fluid, and $v_2$ and $A_2$ are the final speed and cross-sectional area. Show more…

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Water is flowing in a pipe with a varying cross-sectional area, and at all points the water completely fills the pipe. At area, $1,$ the cross-sectional area of the pipe is 0.070 $\mathrm{m}^{2}$ and the magnitude of the fluid velocity is 3.50 $\mathrm{m} / \mathrm{s} .$ What is the fluid speed at points in the pipe where the cross-sectional area is $(a) 0.105 \mathrm{m}^{2},$ (b) 0.047 $\mathrm{m}^{2}$ ?

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Key Concepts

Continuity Equation

The continuity equation is a mathematical statement of the conservation of mass in fluid dynamics, stating that for an incompressible fluid, the product of the fluid’s cross-sectional area and velocity remains constant along its flow. This means if the area increases, the velocity decreases proportionally and vice versa.

Incompressible Flow

Incompressible flow refers to a fluid flow scenario where the fluid density remains constant throughout the flow. This assumption simplifies the conservation of mass analysis and justifies using the continuity equation without needing to account for density variations.

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