The concepts that play roles in this problem are similar tothose in Multiple-Con

Question

The concepts that play roles in this problem are similar tothose in Multiple-Concept Example 15, except the fluid here movesupward rather than remaining horizontal. A liquid is flowingthrough a horizontal pipe whose radius is 0.0234 m. The pipe bendsstraight upward through a height of 5.50 m and joins anotherhorizontal pipe whose radius is 0.0777 m. What volume flow ratewill keep the pressures in the two horizontal pipes the same? Any help is appreciated, thanks The concepts that play roles in this problem are similar tothose in Multiple-Concept Example 15, except the fluid here movesupward rather than remaining horizontal. A liquid is flowingthrough a horizontal pipe whose radius is 0.0234 m. The pipe bendsstraight upward through a height of 5.50 m and joins anotherhorizontal pipe whose radius is 0.0777 m. What volume flow ratewill keep the pressures in the two horizontal pipes the same? Any help is appreciated, thanks

Explanation / Answer

Speed in lower pipe = v1            speed in upper pipe = v2 . You are told the pressures are the same, so using bernoulli'sequation: .     p1   +   (1/2) v12   + gh1   = p2 + (1/2) v22  +   g h2 .                 (1/2) v12    +  0         =         (1/2)v22    + g h2 .        or               v12    =  v22    + 2*9.80*5.50 .           v12   =  v22     +   107.8 . Now... the flow rate through each is speed * area, andarea is   r2   so... .         flow rate 1 = flow rate2         or          v1 * r12 =   v2 * r22 .           v1 * 0.02342   =   v2 *0.07772   . simplify...           v1 =    11.02584 v2 . plug this into the first equation... .        (11.02584v2)2   = v22  + 107.8          121.5684 v22   = v22   + 107.8 .            120.5684 v22   = 107.8              v22 =   0.894098 .     v2 =   0.945568  is the speed in the upper pipe. . flow rate = speed * area = 0.945568 * * 0.07772 =    0.01793m3 /sec = 17.93 liters per second . (note: the second post below is alsocorrect, in principle, but her answer is incorrect becauseshe rounded off too much in her calculations. She wrotethat    (0.0234 / 0.0777)2  is    0.9    but it isactually    0.0907 .   This makes adifference, which is why her answer is slightly different frommine. And hers is incorrect.) . (note: the second post below is alsocorrect, in principle, but her answer is incorrect becauseshe rounded off too much in her calculations. She wrotethat    (0.0234 / 0.0777)2  is    0.9    but it isactually    0.0907 .   This makes adifference, which is why her answer is slightly different frommine. And hers is incorrect.)

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