There are four parts: A, B, C, and D!! Consider the following scenario where wat

Question

There are four parts: A, B, C, and D!!

Consider the following scenario where water is gushing out I of a faucet and being collected into a metal bucket with rectangular opening. This particular physical setup is also mentioned in your lecture (Lecture #3) and you may also want to consult Chapter 12.4 from Physics 124, last year. A. The three situations in Figure 1 show three distinct orientations of the bucket. Note in all three scenarios the jets coming out of the faucets are also equal, as shown by equal blue velocity vectors. The areas of the cross sections 34. of the top of the buckets are also identical in size. The amount of water that flows through a particular area in a fixed time (for example, 1 second) is known as the fluid "flux" through that area. Now answer the following questions 1. Initially all of the buckets are dry. Rank the three buckets in order of water collected after 1 minute, from least to Figure 1 It is convenient to define an area vector A as a vector whose magnitude is equal to the area of a particular surface and whose direction is perpendicular to the surface. We redraw the situation from Figure 1 with the area vector included, as shown to the right in Figure 2. 2. Is the most water collected when A and v are parallel or when they are perpendicular? In which situation is the least water collected? e 90° 0-45 8-0 Figure 2

Explanation / Answer

(A)

1. I, II, III

2. Yes, Most water collected when A is parallel to v. Least water collected when A is perpendicular to v.

(B)

1. I, III, II

2. Yes, it will increase.

(C)

1. II, I, III

2. It increases as we increase the area of the cross-section of the bucket opening.

(D) It's the dot product between A and v which represents the fluid flux (In accordance with what we saw in (A)).

(E) I, III, II

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