- #1

- 35

- 3

## Homework Statement

A pressurized cylindrical tank, 5m in diameter, contains water which emerges from the pipe at point C with a velocity of 25 m/s. Point A is 10m above point B and point C is 3m above point B. The area of the pipe at point B is 0.07 m

^{2}and the pipe narrows to an area of 0.02m

^{2}at Point C. Assume the water is an ideal fluid in laminar flow. The density of water 1000kg/m

^{3}

## Homework Equations

Continuity Equation:

V

_{B}A

_{B}=V

_{C}A

_{C}

Bernouli's equation:

Let D = density of water

P

_{B}+ (1/2)DV

_{B}

^{2}+Dgh

_{B}= P

_{C}+ (1/2)DV

_{C}

^{2}+Dgh

_{C}

## The Attempt at a Solution

Let D = density of water

V

_{B}A

_{B}=V

_{C}A

_{C}

Therefore

V

_{B}=[V

_{C}A

_{C}]/A

_{B}=[25*0.02]/0.07=7.14m/s

P

_{B}+ (1/2)DV

_{B}

^{2}+Dgh

_{B}= P

_{C}+ (1/2)DV

_{C}

^{2}+Dgh

_{C}

Therefore

P

_{B}= P

_{C}+ (1/2)DV

_{C}

^{2}+Dgh

_{C}-(1/2)DV

_{B}

^{2}-Dgh

_{B}

Except P

_{C}and P

_{B}is unknown so this approach shouldn't work. One of my peers claims it is the same as 1 ATM but I'm doubtful since this does not result in answer which is accurate. I don't see how The pressure at Point C could possibly be 1atm... 2 unknowns .. 1 equation.. not going to work :( correct me if wrong.

Upon searching the internet I came across the solution.. which does yield what I firmly believe is the correct answer .. however I don't not understand how this formula came about..

Let D = density of water

P

_{B}= [V

_{C}

^{2}/(2G) - V

_{B}

^{2}/(2G) + y)Dg

=(25

^{2}/(2*9.8) - (7.14

^{2}/(2*9.8) + 3)*1000*9.8

~=~ 316410 Pa ~=~ 320 kPa

It appears to be some variation of the Bernoulli formula but I need to demonstrate how to take those formulas and make them into this format... which I don't even know where to begin. I don't need to know how to derive the formulas that this one came from .. in other words.. I can just say here's the Bernoulli equation .. rearrange and combine like so and obtain this: (without having to derive the Bernoulli equation itself).

Please and thank you.