(a) the liquid flow speed _______ m/s (b) the liquid pressure ______ Pa At a sof

Question

(a) the liquid flow speed
_______ m/s

(b) the liquid pressure
______ Pa

At a soft drink bottling plant, a horizontal section of pipe carrying citric acid in liquid form goes from a cross-sectional area of 8.00 cm2, fluid flow speed of 220 cm/s, and pressure of 1.40 10^5 Pa to a section of pipe with a cross-sectional area of 3.10 cm^2. The density of the citric acid is 1660 kg/m^3. For the section of smaller pipe, determine the liquid flow speed and the liquid pressure. (a) the liquid flow speed _______ m/s (b) the liquid pressure ______ Pa

Explanation / Answer

Solution:

Area A1 = 8 cm^2

velocity = v1 = 220 cm/s

Area A2 =3.1 cm^2

Velocity v2=?

according to equation of continuity,A1v1 = A2 v2

v2= A1v1/A2 =(8)(220)/(3.1)

= 567.7 cm/s = speed thru the 3.1 cm^2 cross section

now according to bernoulli's principle,

P1+1/2 d xv1^2 = P2 + 1/2 d v2^2

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

           = (1.4x10^5 ) +1/2(1660) (2.20^2 - 5.68^2)

        = 1.17 x 10^5 Pa

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