What is the pressure of the fluid at a constriction in a vertical pipe?

[AlvinS]

Homework Statement

An incompressible fluid is flowing through a vertical pipe with a constriction. The wide section is 2.00 cm in diameter and is at the top of the pipe. The pressure of the fluid in the wide section at the top is 200 kPa. The velocity of the fluid in the wide section is 4.00 m/s. The narrow section is 1cm in diameter and is located 2.00 m below the wide section. What is the pressure of the fluid in the narrow section (density of the fluid is 1,000 kg/m3)?

diameter1= 2cm
P1= 200kPa
v1= 4m/s

diameter2=1cm
P2=?
v1=?

height= 2

Homework Equations

Continuity
A1v1=A2v2

Bernoullis equation
.5dv1^2+dgy1+P1= .5dv2^2+dgy2+P2

where d is density, g is gravity, and v is velocity

The Attempt at a Solution

Ugh I've been on this for a long time.
So i found the velocity of V2 by using the continuity equation. I switched all my units to cm then i converted it back to m.

Then i plugged in everything into bernoullis equation and solved for pressure2. this is what i put in.

.5(1000)4^s + 1000(9.8)2 + 200000= .5(1000)16^2 + P2

I came up with an answer but its not one of the mutiple choices. Please put me in the right direction, my last 3 questions are similar and i have a feeling I am doing something totally wrong. I am so tired.. please help, thanx.

 

[Chi Meson]

Your set-up appears to be correct. What is the answer you get?

 

[AlvinS]

I get 99.6kPa.

The choices are:
72 kPa
80 kPa
95 kPa
105 kPa
116 kPa

 

[Chi Meson]

I get what you get. Using g= 10N/kg, I get 100,000 Pa. I believe the selections are incorrect. It happens. Rest assured, you understand the problem. What are some of the other "wrong" ones?

 

[AlvinS]

An incompressible fluid is flowing through a pipe with a constriction. The pipe is on an incline with an angle of 20.0 degrees. The narrow section is 15.0 m from the wide section and the narrow section is lower than the wide section. The velocity of the fluid in the wide section of the pipe is 6.00 m/s and the velocity of the fluid in the narrow section of pipe is 9.00 m/s. The pressure of the fluid in the wide section is 250 kPa. What is the pressure in the narrow section of the pipe (density of the fluid is 1,000 kg/m3)?

For this one i found the height by

15cos20= 5.13

Then i just plugged in everything into bernoulli's equation.

.5(1000)6^2 + 1000(9.8)5.13 + 250000 = .5(1000)9^2 + P2

I got like 277 kPa, which when i think about it doesn't make sense because i though greater velocity resulted in less pressure, then again the whole gravity thing. I don't know anymore! I am so tired, its 4am, i live in japan. And i have exam on this stuff tomorrow. I am pretty mad that the selections are incorrect, but please check meon this one.

The selections for this problem are:
228 kPa
203 kPa
195 kPa
167 kPa
145 kPa

 

[Chi Meson]

I got like 277 kPa, which when i think about it doesn't make sense because i though greater velocity resulted in less pressure, then again the whole gravity thing. I don't know anymore! I am so tired, its 4am, i live in japan. And i have exam on this stuff tomorrow. I am pretty mad that the selections are incorrect, but please check meon this one.

The selections for this problem are:
228 kPa
203 kPa
195 kPa
167 kPa
145 kPa

You are again correct. Get some sleep. THe increased velocity tends to decreas the pressure, but the additional depth more than makes up for it. That is, the 5 m of depth causes more increase in pressure than the additional speed.

You understand it. Get some sleep!