Water is moving with a speed of 6.2 m/s through a pipe with across-sectional are

Question

Water is moving with a speed of 6.2 m/s through a pipe with across-sectional area of 4.1 cm2. The water graduallydescends 9.5 m as the pipe increases to 7.8 cm2.(a) What is the speed at the lower level?(b) If the pressure at the upper level is 1.5× 105 Pa, what is the pressure at the lowerlevel? a) 3.26 m/s Water is moving with a speed of 6.2 m/s through a pipe with across-sectional area of 4.1 cm2. The water graduallydescends 9.5 m as the pipe increases to 7.8 cm2.(a) What is the speed at the lower level?(b) If the pressure at the upper level is 1.5× 105 Pa, what is the pressure at the lowerlevel? a) 3.26 m/s

Explanation / Answer

(b). From Bernoulli's theorem , P + gh + ( 1/ 2) v ^2 = P ' +gh ' + ( 1/ 2) v ' ^ 2 Given h = 0          h ' =9.5 m          v = 3.26 m /s          v ' = 6.2 m /s           =density of water = 1000 kg / m ^ 3         P ' = 1.5 ×105 Pa So, pressure at lower level = P + g ( h ' - h ) + (1/ 2) [ v ' ^ 2 - v ^ 2 ]                                         = ( 1.5 × 105 Pa ) + ( 1000 * 9.8 * 9.5 ) + ( 0.5* 1000 * ( 6.2 ^ 2-3.26 ^ 2 ) )                                        = ( 1.5 × 105 Pa) + 93100 + 13906.2                                        = 2.57 * 10 ^ 5 Pa

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