Blending Liquids

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Don Shearman

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Don Shearman 11 months, 3 weeks ago

Published this.

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Don Shearman 2 years ago

Created this as a copy of Reaction forces.

Name	Status	Author	Last Modified
Reaction forces	Ready to use	Don Shearman	08/05/2024 06:12
Electronic circuit	Ready to use	Don Shearman	17/04/2024 02:20
Blending Liquids	draft	Don Shearman	16/04/2024 03:07
Electronic circuit 2	draft	Don Shearman	17/04/2024 02:24

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

vol	number	4
conc	number	0.15
conc_1	number	0.1
conc_2	number	0.29

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..4 #0.5)

JME function reference

Description

Total volume of solution being blended

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `number`

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap $v_1$ Number entry
  Add
2. Gap $v_2$ Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

An environmental engineer need to blend a single mixture of insecticide spray of volume $V=\var{vol}$ litres and concentration $C=\var{conc}$ from two solutions having concentrations $c_1=\var{conc_1}$ and $c_2=\var{conc_2}$ . If the volumes of each solution are $v_1$ and $v_2$ we have the following system of equations:

$\begin{align} v_1+v_2-\var{vol}&=0\\\var{conc_1}v_1+\var{conc_2}v_2&=\var{conc*vol}\end{align}$

Find the volumes $v_1$ and $v_2$ of the solutions required to make up the mixture. Give your answer correct to 3 decimal places and show full working in your handwritten notes.

$v_1=$ $v_1$ litres

$v_2=$ $v_2$ litres

Advice

We need to solve

$\begin{align} v_1+v_2 - \var{vol} &=0\\\var{conc_1}v_1 +\var{conc_2}v_2 &=\var{conc*vol}\end{align}$ which can be written as

$\begin{align} v_1+v_2 &= \var{vol}\quad (1)\\ \var{conc_1}v_1 +\var{conc_2}v_2 &=\var{conc*vol}\quad (2)\end{align}$

Using the method of elimination to eliminate $v_2$ we multiply equation $(1)$ by $-\var{conc_2}$ to get

$\begin{align}-\var{conc_2}v_1-\var{conc_2}v_2 &= -\var{conc_2*vol}\quad (3)\\ \var{conc_1}v_1 +\var{conc_2}v_2 &=\var{conc*vol}\quad (4)\end{align}$

Taking $(3)+(4)$ we obtain

$\var{conc_1-conc_2}v_1=\var{(conc-conc_2)*vol}$

and hence

$v_1=\var{((conc-conc_2)*vol)/(conc_1-conc_2)}$

Substituting this into $(1)$ gives us

$\var{((conc-conc_2)*vol)/(conc_1-conc_2)}+v_2 = \var{conc*vol}$ and hence

$v_2=\var{((conc-conc_2)*vol)/(conc_1-conc_2)}$

Thus the volumes are $v_1\approx\var{precround(((conc-conc_2)*vol)/(conc_1-conc_2),3)}$ litres and $v_2\approx\var{precround(((conc-conc_2)*vol)/(conc_1-conc_2),3)}$ N.

(Note that this problem could also be solved by eliminating $v_1$ instead of $v_2$ or by the method of substitution, however the final answers will be the same.)

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This question is used in the following exam:

Class Test 1 by Don Shearman in MfEP Progress Quizzes.

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Taxonomy: mathcentre

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Don Shearman 11 months, 3 weeks ago

Don Shearman 2 years ago

Error in variable testing condition

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Generated value: `number`

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Blending Liquids

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Don Shearman 11 months, 3 weeks ago

Don Shearman 2 years ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`