1. Fresh water flows through a horizontal tapered pipe. At the wide end its spee

Question

1. Fresh water flows through a horizontal tapered pipe. At the wide end its speed is 9 m/s. The difference in pressure between the two ends is 5395 Pa. What is the speed (in m/s) of the water at the narrow end? Round your answer to the nearest tenth.

2.A uniform plank is 9-m long and weighs 92 N. It is balanced on a sawhorse at its center. An additional 187 N weight is now placed on the left end of the plank. To keep the plank balanced, it must be moved what distance (in m) to the right? Round your answer to the nearest tenth.

3.A star of uniform mass with a radius R rotates about its diameter with angular momentum L. Under the action of internal forces the star collapses until its radius is one fourth of its initial size. The magnitude of its new angular momentum is:

a. 4L        b. L/4      c.L      d. L/16        e. 16L

Explanation / Answer

1) The Bernoulli equation is a 'conservation of energy' equation
so
there is equality at both ends of the pipe

(P + (1/2 rho v^2) + (rho g h)_1 = (P + (1/2 rho v^2) + (rho g h)_2
the pipe is horizontal so the rho g h terms drop out
(pressure is lower at the narrow end where v is higher so let P1 and v_1 be at the wide end)
P1 - P2 = 1/2*rho ( (v_2)^2 - (v_1)^2) )
5395 Pa = 1/2*(1000 kg/m^3) * ((v_2)^2 - (9.0 m/s)^2)
(v_2)^2 = 97.79
v_2 = 9.58 m/s

2) It should be brought to the center of the plank and hence should move 4.5m

3) Since it is not being acted by any external torque it remains constant hence answer is C

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