At a soft drink bottling plant, a horizontal section of pipe (i.e., the height o

Question

At a soft drink bottling plant, a horizontal section of pipe (i.e., the height of the pipe does not change) carrying citric acid in liquid form goes from a cross-sectional area of 8.00 cm2, fluid flow speed of 2.90 m/s, and pressure of 1.40 105 Pa to a section of pipe with a cross-sectional area of 4.00 cm2. The density of the citric acid is 1660 kg/m3. For the section of smaller pipe, determine the liquid flow speed and the liquid pressure.

(a) the liquid flow speed HINT: You can keep both areas in units of cm2 when using the continuity equation. m/s (b) the liquid pressure Pa

Explanation / Answer

A1 = 8 cm^2, A2 = 4cm^2, v1 =2.9 m/s, P1 =1.4x10^5 Pa, d =1660 kg/m^3

(a) Volume flow rate is constant

A1v1 =A2v2

v2 = (8/4)(2.9) = 5.8 m/s

(b) From Bernoul's theorem

P1 +(1/2)dv1^2 =P2 +(1/2)dv^2

P2 = P1 +(1/2)d [v1^2 -v2^2]

P2 = (1.4x105) + (0.5*1660)[(2.9*2.9) - (5.8*5.8)]

P2 = 1.191x105 Pa

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