You will start by getting used to the idea of the linear mass density by relating it to concepts you are already familiar with: the mass and the (volume mass) density. First, you have a column of pure water that has a density PH20= 1 g/cc. The water column is in a cylinder. The column has cross-sectional area 31 cm2 and height 75 cm before salt is added. The linear mass density has two different definitions. One is going up in dimensionality, that is from the volume mass density p to the linear mass density A λ = PA where A is the cross-sectional area of the object. The other is going down in dimensionality, that is from the mass down to the linear mass density A = M where H is the height of the column in our case. You will use both of these below: (a) What is the linear mass density of the water column? ÅH20 = (b) What is the mass of the water? M = Let's now try this after adding salt to the water. When we do, the column's height rises to a level 78 cm, and we measure its salinity to 54.5 9Naci/k9H20 (grams of salt per kilogram of water). Assume that the solution is well-stirred at this point so that the salt is uniformly distributed.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
icon
Related questions
Question
You will start by getting used to the idea of the linear mass density by relating it to concepts you are already familiar with: the mass and the (volume mass) density.* First, you have a column of pure
water that has a density PH₂0 = 1 g/cc. The water column is in a cylinder. The column has cross-sectional area 31 cm² and height 75 cm before salt is added.
The linear mass density has two different definitions. One is going up in dimensionality, that is from the volume mass density p to the linear mass density
λ = PA
where A is the cross-sectional area of the object. The other is going down in dimensionality, that is from the mass down to the linear mass density
λ = M
H
where H is the height of the column in our case. You will use both of these below:
(a) What is the linear mass density of the water column?
ÅH20 =
(b) What is the mass of the water?
M =
Let's now try this after adding salt to the water. When we do, the column's height rises to a level 78 cm, and we measure its salinity to 54.5 9Naci/k9H20 (grams of salt per kilogram of water). Assume
that the solution is well-stirred at this point so that the salt is uniformly distributed.
We can now find the various quantities for the salt water, in reverse order.
(c) First, use dimensional analysis to find the mass of the salt water column.
M' =
(d) Next, find the linear mass density of the salt water column.
A' =
(e) Finally, find the volume mass density.
p' =
You should, at this point conjecture how to find the linear mass density of the salt water from the linear mass density of the pure water using only the salinity. Does your idea make sense physically? If
you implement it, does it match the value found in part (d)?
Transcribed Image Text:You will start by getting used to the idea of the linear mass density by relating it to concepts you are already familiar with: the mass and the (volume mass) density.* First, you have a column of pure water that has a density PH₂0 = 1 g/cc. The water column is in a cylinder. The column has cross-sectional area 31 cm² and height 75 cm before salt is added. The linear mass density has two different definitions. One is going up in dimensionality, that is from the volume mass density p to the linear mass density λ = PA where A is the cross-sectional area of the object. The other is going down in dimensionality, that is from the mass down to the linear mass density λ = M H where H is the height of the column in our case. You will use both of these below: (a) What is the linear mass density of the water column? ÅH20 = (b) What is the mass of the water? M = Let's now try this after adding salt to the water. When we do, the column's height rises to a level 78 cm, and we measure its salinity to 54.5 9Naci/k9H20 (grams of salt per kilogram of water). Assume that the solution is well-stirred at this point so that the salt is uniformly distributed. We can now find the various quantities for the salt water, in reverse order. (c) First, use dimensional analysis to find the mass of the salt water column. M' = (d) Next, find the linear mass density of the salt water column. A' = (e) Finally, find the volume mass density. p' = You should, at this point conjecture how to find the linear mass density of the salt water from the linear mass density of the pure water using only the salinity. Does your idea make sense physically? If you implement it, does it match the value found in part (d)?
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Dimensional Analysis
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY