Semantics making Bernoulli's Eq KILLER see if you can make sense

[missnola2a]

**semantics making Bernoulli's Eq KILLER! see if you can make sense

Homework Statement

a pipe that carries a fluid ρ = 873 kg/m3 lies along the slope of a smooth hill which is 140 m high. The speed of the liquid at the bottom of the hill is 6.5 m/s. The diameter of the crude oil pipe line at the top of the hill reduces by a factor 5. Please answer the following:
Hint
(a) By what factor the area of the oil pipe line reduces at the top of the hill?

(b) What is the ratio of speeds of the oil from the bottom of the hill to the top of the hill?

(c) How much potential energy per unit volume the oil gains as it moves from the bottom to the top of the hill?
J/m3
(d) What is the change in pressure in the pipe line during this motion along the hill?

Homework Equations

The Attempt at a Solution

OK ... so I first of all am confused by this because I can't tell if the pipe starts at the bottom of the hill and goes up or vice versa.

This may not matter mathematically, but I am a conceputal person.

That said,
a1v1=a2v2

(pie drops out)
r1^2 v1= r2^2 v2

this is where i am a little stuck, should it be 5r1=r2
OR r2=r1/5

this changes the equation a lot. after I get v2 (or v1) I put it into origional

P1 + 1/2 rho V1^2 + rho*g*Y1 = P2 + 1/2 rho V2^2

*** assuming that PE for 2 is 0, but again, i am confused as to where in the system Y=0

thanks for your help

 

[minger]

Well, first you could assume that the pipe starts at the top and then see if there is enough kinetic energy to make it to the top. Also, it says that the diameter of the crude oil pipe line at the top of the hill reduces by a factor 5

So, the diameter at the top of the hill is 5 times smaller than at the bottom.