(a) Consider a stream of liquid of density rho with speed v_(1) passing abruptly from cylindrical pipe of cross-sectional area a_(1) into a wider cylindrical pipe of cross-sectional area a_(2) (see figure). The jet will mx the surrounding fluid and, after the mixing, will flow on almost uniformly with an average speed v_(2). Without referring to the details of the mixing use momentum ideas to show that the increase in pressure due to the mixing is approximately P_(2) - P_(1) = rho v_(2)(v_(1)-v_(2)) (b) Show from Bernoulli's principle h that in a gradually widening pipe we would get P_(2) - P_(1) = (1)/(2)rho (v^(1)^(2)-v_(2)^(2)) and explain the loss of pressure [the difference is (1)/(2) rho(v_(1)-v_(2))^(2)] due to the abrupt enlargement of the pipe. can you draw an analogy with elastic and inelastic collisions in particle mechanics ?

(a) Consider a stream of liquid of density rho with speed v_(1) passin

1.	(a) Consider a stream of liquid of density rho with speed v_(1) passing abruptly from cylindrical pipe of cross-sectional area a_(1) into a wider cylindrical pipe of cross-sectional area a_(2) (see figure). The jet will mx the surrounding fluid and, after the mixing, will flow on almost uniformly with an average speed v_(2). Without referring to the details of the mixing use momentum ideas to show that the increase in pressure due to the mixing is approximately P_(2) - P_(1) = rho v_(2)(v_(1)-v_(2)) (b) Show from Bernoulli's principle h that in a gradually widening pipe we would get P_(2) - P_(1) = (1)/(2)rho (v^(1)^(2)-v_(2)^(2)) and explain the loss of pressure [the difference is (1)/(2) rho(v_(1)-v_(2))^(2)] due to the abrupt enlargement of the pipe. can you draw an analogy with elastic and inelastic collisions in particle mechanics ?
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