Finding pressure at narrow end of segment

[sona1177]

Homework Statement

A horizontal segment of pipe tapers from a cross-sectional area of 50.0 cm^2. The pressure at the larger end of the pipe is 1.20 x 10^5 Pa and the speed is .040 m/s. What is the pressure at the narrow end of the segment?

Homework Equations

I know how to do the problem using Bernoulli's equation but why can't I manage to get the correct answer using P=rho(g)(d). where rho=1000, g=9.8, and d=.00798 m

The Attempt at a Solution

 

[Stonebridge]

Could you explain what d is in your equation.
As the pipe is horizontal there is no potential energy consideration.
I also note that there is no information given about the change in the cross section area.
Maybe you could clarify the question?

 

[sona1177]

Could you explain what d is in your equation.
As the pipe is horizontal there is no potential energy consideration.
I also note that there is no information given about the change in the cross section area.
Maybe you could clarify the question?

d is the length of the narrow segment which I obtained by dividing area/pi and taking the sq root to get the radius. I then multiplied that by 2.

 

[sona1177]

Could you explain what d is in your equation.
As the pipe is horizontal there is no potential energy consideration.
I also note that there is no information given about the change in the cross section area.
Maybe you could clarify the question?

Ooops! Sorry about leaving that info out. It tapers from 50-> 5 cm^2

 

[Stonebridge]

I don't quite understand what you are doing here.
The expression ρhg in the Bernoulli formula includes the terms
ρ the density of the fluid
g acceleration due to gravity
h the height of the liquid above the reference level
You have written ρdg but stated that d is "the length of the narrow segment". However, your calculation looks like it is for the diameter of the narrow segment.
Neither of these values, length or diameter, are the ones in the expression.
As the tube is horizontal, you don't need this term anyway, you just need the terms
½ρv² and p to find the pressure.
The value of v is found from the volume flowing per second being equal in both parts of the tube.