(b) A 10 kL tank of water provides water for a small village. Water is drunk from the tank at a rate of 1000 L per day, and the water is replenished at the same rate. Unfortunately, the filter/purifier for the intake water is malfunctioning. Conse- quentially the water that is replenishing the tank is contaminated; it contains 0.00125 mg/L of heavy metals. Suppose that when the contamination was discovered the tank was 3/4 full and contained a, mg of heavy metals. (i) Find a formula, A(t), for the amount of heavy metals in the tank at time t. Hint: make sure your units are consistent for all quantities. We suggest mg/kL If the concentration of heavy metals in the water is below 0.001 mg/L then the water is still safe to drink. You may assume that the heavy metals in the tank are well mixed (and thus evenly distributed) in the tank. The maintenance company has been notified, and have indicated that the they'll be on premises to service the filter/purifier in 7 days (and please make sure some- body is on premises during that entire day). However, we know from experience that they can be anywhere up to 3 days late. (ii) If the initial amount of heavy metals in the tank was 2 mg, will the concen- tration reach dangerous levels before the company services the tank? (Yes, no, or maybe?). Justify your answer. (iii) What is the largest initial amount of heavy metals that will definitely not reach dangerous levels before the company services the tank?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

(b) A 10 kL tank of water provides water for a small village. Water is drunk from the
tank at a rate of 1000 L per day, and the water is replenished at the same rate.
Unfortunately, the filter/purifier for the intake water is malfunctioning. Conse-
quentially the water that is replenishing the tank is contaminated; it contains
0.00125 mg/L of heavy metals.
Suppose that when the contamination was discovered the tank was 3/4 full and
contained a, mg of heavy metals.
(i) Find a formula, A(t), for the amount of heavy metals in the tank at time t.
Hint: make sure your units are consistent for all quantities. We suggest mg/kL
If the concentration of heavy metals in the water is below 0.001 mg/L then the
water is still safe to drink. You may assume that the heavy metals in the tank
are well mixed (and thus evenly distributed) in the tank.
The maintenance company has been notified, and have indicated that the they'll
be on premises to service the filter/purifier in 7 days (and please make sure some-
body is on premises during that entire day). However, we know from experience
that they can be anywhere up to 3 days late.
(ii) If the initial amount of heavy metals in the tank was 2 mg, will the concen-
tration reach dangerous levels before the company services the tank? (Yes,
no, or maybe?). Justify your answer.
(iii) What is the largest initial amount of heavy metals that will definitely not
reach dangerous levels before the company services the tank?

Expert Solution

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

Step 1

Please explain how you can confirm 1.25mg of heavy metals are consumed per day? It seems to me that this is only true once the contamination of the tank reaches 0.00125m/L.

My thinking is this:

Assume the tank begins with a heavy metal concentration lower than 1.25mg/L.

Introducing 1kL of water with concentration 1.25mg/kL to a 7.5kL supply results in:

8.5kL of water, and 1.25mg of heavy metals

Therefore the supply's concentration = 1.25mg/8.5kL

And removing 1kL results in the tank having the same concentration (1.25mg/8.5kL). The question expects you to assume the tank is well mixed.

Also, I acknowledge that this thinking assumes that the contaminated water is all added before any water is removed, which is an incorrect assumption, but it just demonstrates where my confusion is.

Solution