1 The Reynolds Transport Theorem can be expressed as DB Dt

1. The Reynolds Transport Theorem can be expressed as, DB Dt = t Z V bdV + Z S bV~ · ndA. ˆ

In fluid mechanics, B is most often chosen to be the mass, momentum, or kinetic energy of the fluid. However, B can represent many other quantities, such as algae in the ocean. In this problem, we will examine one such application.

Portage Bay, which is the body of water next to Harris Hydraulics Laboratory, is fed by Lake Washington through the Montlake Cut, and drains into Lake Union, and eventually Puget Sound. When Portage Bay accumulates too much nutrients, it can suffer from algal blooms, where algae rapidly grow and choke out other life. We will model such a bloom with the Reynolds Transport Theorem.

Note: the most important aspect of this assignment is your reasoning and the process. Explain your work thoroughly. Portage Bay is nicely bounded by the Montlake Bridge to the east and the I-5 bridge to the west, so we will use these as the outlet and inlet for our control volume. Suppose we know that the current at the Montlake Bridge is a uniform value C1 and the cross sectional area of the channel is A1. The outlet at the I-5 bridge is also assumed to have an area A2, with an unknown uniform outlet current. Portage Bay has a surface area of S, and the water level, due to recent rains, is increasing at a rate of R meters per second.

a) Use the Reynolds Transport Theorem to find an expression for the outflow under the I-5 bridge.

b) Now we’ll consider the algae. Algae, to a first order approximation, can be assumed to follow the current of the water that it is in. Let B represent the total cells of algae in Portage Bay. What does b represent? What are its units?

d) Suppose that algae grows according to the following law, for time in seconds: db dt = 103 b 106 With this knowledge, how does our expression for DB Dt change?

e) What is the theoretical maximum amount of algae, b? (Give a numerical answer). The residence time of a body of water is the amount of time it would take to completely replace all of the water. It may be approximated as the volume of the body, divided by the inflow. How low of a residence time would cause you to worry about this algal bloom? Note: there is no numerical answer here; we are looking for qualitative arguments based on scaling and your knowledge of the Reynolds Transport Theorem

Solution

Solution:-

The two important changes in geriatrics:

As the age increases, older adults develop two kinds of developmental changes in their minds in order to cope up with losses and changes in their lives. They are:

Trying to maintain control in everything they need to do
Create a legacy
Establishing and maintaining control:

We all know that as the age increases, old age people encounter many changes like changes in physical, psychological and emotional health, changes in physical activity, etc. In addition to this, they also experience multiple losses like a decline in functioning or mobility, loss of family members (i.e. separation of their family members by the split of an extended family into a nuclear family), loss of friends, property or material possessions, social status, etc.

In order to cope up with these changes and losses, they prefer to take control in activities they do. That is, they prefer to have more autonomy and like to make decisions by themselves rather than being directed to an imposed decision by their family members. This is a normal part of the coping mechanism.

It is the responsibility of adults (sons and daughters) to identify their parents’ (old age peoples’) needs and problems and establish appropriate ways to meets their requirements. According to the text, we need to listen for these cues through verbal cues where geriatrics express their willingness or desire to do something or prefer autonomy to do an activity. In such cases, we must respect their ‘control behaviour’ and act accordingly. For example, instead of saying “you must or have to do this/that”, we must encourage the old-aged “you choose/take a decision”, “you manage this task”, etc. By doing so, they get appreciated, take an active part in decision making, develop confidence and feel more satisfied in their lives.

Creating a Legacy:

As a part of the normal ageing process, they try to leave their foot-prints to their younger generations (their sons and daughters) through reminiscing old events, telling past stories of themselves repeatedly. They feel that they are conveying the young with life events, instructions to lead a peaceful life, to redeem from past mishappenings or mistakes and to remember them forever.

As per the text, it is the responsibility of the loved ones to put more enthusiastic questions to them and is eager to listen to their talks during a conversation. By this way, they feel that we are giving a choice to explore their minds before their end of life.

a) Predict Rating Y = -37.7775 + 0.02190 X

Given X = 1853

Predict Rating Y = -37.7775 + 0.02190 (1853) = 2.8032

Residual : 2.8032 - 4.57 = -1.7668

(b) If you add the covered bridge to the data the slope will be decrease

(c)

If you add the covered bridge to the data the R2 will be increase

(d)

Given X = 1853

Predict Rating Y = -37.7775 + 0.02190 (1972) = 5.4093

Error = 5.4093 - 4.57 = 0.8393