Question

In a horizontal water pipe that narrows to a smaller radius, the velocity of the water in the section with the smaller radius will be larger. What happens to the pressure? a) The pressure will be the same in both the wider and narrower sections of the pipe. b) The pressure will be higher in the narrower section of the pipe. c) The pressure will be higher in the wider section of the pipe. d) It is impossible to tell.

Name: Problem 6, Chapter 13: University Physics with Modern Physics
Uploaded: 2021-05-22T16:24:43-08:00
Duration: 1 min 36 s
Channel: Ajay Singhal

   In a horizontal water pipe that narrows to a smaller radius, the velocity of the water in the section with the smaller radius will be larger. What happens to the pressure?
a) The pressure will be the same in both the wider and narrower sections of the pipe.
b) The pressure will be higher in the narrower section of the pipe.
c) The pressure will be higher in the wider section of the pipe.
d) It is impossible to tell.

University Physics with Modern Physics

Wolfgang Bauer, Gary… 2nd Edition

Chapter 13, Problem 6

Instant Answer

Solved by Expert Ajay Singhal

05/22/2021

Step 1

The velocity of the water in the section with the smaller radius is larger. This is given by the continuity equation, which states that the product of the cross-sectional area and the velocity of the fluid is constant. Mathematically, this can be written Show more…

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In a horizontal water pipe that narrows to a smaller radius, the velocity of the water in the section with the smaller radius will be larger. What happens to the pressure? a) The pressure will be the same in both the wider and narrower sections of the pipe. b) The pressure will be higher in the narrower section of the pipe. c) The pressure will be higher in the wider section of the pipe. d) It is impossible to tell.

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Key Concepts

Continuity Equation

The Continuity Equation in fluid dynamics asserts that for an incompressible fluid, the mass (or volumetric) flow rate remains constant along a streamline. This means that if the cross-sectional area of the pipe decreases, the velocity of the fluid must increase proportionally to conserve the flow rate.

Bernoulli's Principle

Bernoulli's Principle states that in a steady, incompressible, and frictionless flow, the sum of the pressure energy, kinetic energy, and potential energy per unit volume remains constant along a streamline. Consequently, in regions where the fluid velocity increases (such as in a narrower section of a pipe), the pressure decreases, and vice versa.

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