How Does Gingerale's Pressure Change in Descending Pipes?

[ashwinanand]

Homework Statement

Gingerale (ρ=1100 kg/m3) moves through a system of pipes in a beverage factory. Initially, it travels through a pipe with a cross-sectional area of 3.80 cm2 at a speed of 4.77 m/s. Gradually, the gingerale descends by 8.49 m while the pipe's cross-sectional area increases to 8.15 cm2. The speed of the gingerale at the lower level is 2.22m/s. What is the pressure at the lower level if the pressure in the upper level is known to be 1.50x10^5Pa?

Homework Equations

delta P = P2-P1

P1+(1/2)*rho*(v^2)+rho*g*y

upper level pressure=1.50x10^5Pa

The Attempt at a Solution

P1 + 0.5(1100kg/m^3)(4.77m/s^2)+(1100)(9.8m/s^2)(8.49m)=P2 + 0.5(1100)(2.22m/s^2)+(1100)(9.8m/s^2)(8.49m)
P1 + 1.04x10^5=P2 + 9.42x10^4

(deltaP)P2-P1=9.80x10^3Pa

upper level pressure- deltaP
1.50x10^5Pa-9.80x10^3Pa = 1.40x10^5Pa


I am confused of if I had used bernoulli's equation right and if the proper height was used. I can't seem to get the right pressure.

 

[yinx]

P1+(1/2)*rho*(v^2)+rho*g*y

this is part of bernoulli's equation and it's correct.

P1 + 0.5(1100kg/m^3)(4.77m/s^2)+(1100)(9.8m/s^2)(8.49m)=P2 + 0.5(1100)(2.22m/s^2)+(1100)(9.8m/s^2)(8.49m)
P1 + 1.04x10^5=P2 + 9.42x10^4

you applied the same height of "8.49m" on both sides of the equation.
If you do this, it means that "the height of the pipe remains the same throughout. ie. its a horizontal pipe parallel and 8.49m above the ground"
however, The question states that the gingerale decended by 8.49m. (height on both side of the equation shd not be the same then, there should be a height difference of 8.49m)

Therefore, we can take a reference point: the lower level as height 0.00m and upper level as height 8.49m.

therefore, rho*g*y at the right side should be equals 0, because we take reference of height. y=0 at the lower level.

What is the pressure at the lower level if the pressure in the upper level is known to be 1.50x10^5Pa?

Its given that level at upper level is 1.50x10^5 pa, this means that P1 in the bernoulli's equation is 1.50X10^5 and they are asking you to find p2.

Plug in all the relevant numbers and recalculate.