(a) Show that the expression for the speed of the liquid leaving the pipe is V₁ = √2gh

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)...
icon
Related questions
Question

 Show that the expression for the speed of the liquid leaving the pipe is

?1 = √2?ℎ

Solution:
(a) Show that the expression for the speed of the liquid leaving the pipe is
v₁ = √2gh
From the Bernoulli's equation
1
P₁ + pv² + pgy₁ = P₂ +
pv² + pgyz
1
1
P₁ − P₂ + pv² + pgy₁ = =pv² + pgyz
Since the pressures at points 1 and 2 are the same, P1 = P2, then P1 - P2 = 0.
1
1
0+pv² +pgy₁ = pv² + pgy₂
1
1
pv² +pgy₁ =pv² +pgyz
- continue until you arrive at
v₁ = √2gh
Additional hint: h = y2-y₁ and if the tank is very large, the liquid level changes only slowly, and the speed
at point 2 can be set equal to zero (V₂ = 0).
Transcribed Image Text:Solution: (a) Show that the expression for the speed of the liquid leaving the pipe is v₁ = √2gh From the Bernoulli's equation 1 P₁ + pv² + pgy₁ = P₂ + pv² + pgyz 1 1 P₁ − P₂ + pv² + pgy₁ = =pv² + pgyz Since the pressures at points 1 and 2 are the same, P1 = P2, then P1 - P2 = 0. 1 1 0+pv² +pgy₁ = pv² + pgy₂ 1 1 pv² +pgy₁ =pv² +pgyz - continue until you arrive at v₁ = √2gh Additional hint: h = y2-y₁ and if the tank is very large, the liquid level changes only slowly, and the speed at point 2 can be set equal to zero (V₂ = 0).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 3 images

Blurred answer
Knowledge Booster
Density of fluid
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON