A sprinkler essentially consists of a pipe AB mounted on a hollow shaft. The wat

Question

A sprinkler essentially consists of a pipe AB mounted on a hollow shaft. The water comes in the pipe at O and goes out the nozzles at A and B, causing the pipe to rotate. Assume the the particles of water move through the pipe at a constant rate relative to the pipe of 2 ft/s and that the pipe AB is rotating at a constant angular velocity of 250 rpm. In all cases , express the answers using the righ-handed orthagonal component system. Determine the acceleration of the water particles that are at a distance d/2 from O (still within the horizontalportion of the pipe. Let d=9 inches.

Answer should be in the form a = (xxx)uc + (xxx)ub  ft/s2. ub and uc are unit vectors.

Explanation / Answer

the angular velocity is

w = 250 rpm = 250 x (2pi/60) rad/s

we know that

w^2 - wo^2 = 2A x theta   (A ------ alpha)

or A = (w^2 - wo^2/2theta)

where wo = 0 and theta = 2pi radians

Also,the tangential acceleration is

a_t = r x A

where r is radius vector

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