Quiz1A

# Quiz1A - I a = I b I a = A a v a current that flows through...

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Quiz1A DL Sec Grading: Last 6 digit of student ID: Name: First three letters of your family name 1. Consider two pipes shown in the diagrams below. For Pipe 1, the water enters from the left end ( labeled a on the diagram) at a speed of 6 m/s , and flows through a point b and to the rest of the fluid circuit (not shown). Similarly for Pipe 2, the water enters from the left end ( labeled c on the diagram) at a speed of 6 m/s , and flows through a point d and to the rest of the fluid circuit (not shown). You can assume that the fatter sections of both pipes have no dissipation, however, narrower sections have significant resistances given by R b (for Pipe 1) and R d (for Pipe 2).We know the pressures at point a and c are equal and given by 1.075 x 10 5 Pascals . The areas of the pipes are given on the diagram. Pipe 1 Pipe 2 R b A b = 50 cm 2 v a = 6m/s a b A a =100 cm 2 d A d = 25 cm 2 v c = 6m/s c A c = 100 cm 2 R d (Note R d > R b ) (a) Current conservation (applied to Pipe 1) tells you that
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Unformatted text preview: I a = I b ( I a = A a v a : current that flows through point a ). (i) Find the fluid velocity v b at point b . (ii) Apply current conservation to Pipe 2 and find v d at point d . (b) Is the pressure at point b greater or smaller than the pressure at point a ? Briefly explain your answer. Hint : Energy density equation is given by : ∆ P + (1/2) ρ ∆ (v 2 ) + ρ g ∆ y + IR = E pump /volume (c) How does pressure at point b and point d compare? Circle your response and explain your answer using the energy density model. (Hint: Remember Pipe 1 and Pipe 2 are two separate fluid systems!) { P b = P d , P b < P d , P b > P d } (d) Suppose we want to have P b = P d . One way to realize this is to add a pump to one of the pipes. Which pipe (Pipe 1 or Pipe 2) would you add the pump to? Explain your answer Briefly and Clearly....
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