Question

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 330 cm/s, and pressure of 1.40 105 Pa to a section of pipe with a cross-sectional area of 3.60 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.

Answer 1

Given

Area1 = A1 = 8cm^2

Area2 = A2 = 3.60cm^2

Speed1 V1= 330cm/s = 3.3 m/s

By continuity equation

A1V1 = A2V2

8x330 = 3.60xV2

V2 = (8x330)/3.60

V2 = 733.33 cm/s

V2 = 7.3m/s

Now part 2

since both the section is at same level therefore z=z' =0

Now let use bernoulis equation

P/ρg + v^2/2g + z = P2/ ρg + (V2)^2/2g +z'

(1.40x10^5)/(1660x9.8) + (3.3^2)/(2x9.8)+ 0 = P2/1660x9.8 + 7.33^2/2x9.8 +0

8.606 + 0.555 = P2/16268 + 2.741

P2 = 6.42x16268

P2 = 1.0444x10^5 pa