An incompressible fluid is flowing through a vertical pipe with a constriction.

Question

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 located 4.00 m below the wide section. What is the diameter of the narrow section for the pressure of the fluid in the narrow section to equal the pressure in the wide section? (density of the fluid is 1000 kg/m3) A) 1.50 cm B) 1.36 cm C) 1.28 cm D) 1.12 cm E) 1.00 cm

Explanation / Answer

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

diameter2=1cm
P2=?
v1=?

height= 2

2. Relevant 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

3. The attempt at a solution

Ugh ive 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

P2 = 95 KPa

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