Calculating Pressure in a Narrowed Pipe

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Water flows through a horizontal pipe that narrows from a 10 cm diameter to a 5 cm diameter, with a pressure gauge reading of 50 kPa in the narrow section. To find the pressure in the wider section, Bernoulli's equation is applicable, as it relates pressure and velocity in fluid dynamics. The velocity in the narrow section is four times that in the wider section due to the area change. The relevant equations include the continuity equation (A1V1 = A2V2) and the pressure difference equation (P1 - P2 = 1/2 (density) (V2^2 - V1^2)). Understanding these principles leads to the correct pressure reading of 5.34 x 10^4 Pa in the wider section.
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Homework Statement



Water flows at through a horizontal pipe that narrows smoothly from 10 cm diameter to 5.0 cm diameter. A pressure gauge in the narrow section reads 50 kPa.

What is the reading of a pressure gauge in the wide section

Homework Equations



A_1*F_1=A_2*F_2

The Attempt at a Solution



I tried to use this equation and it didn't work. I already know the answer is 5.34 x 10^4 but I need to know how to get that answer.
 
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Do you know bernoulli's eqn. I think that is what is needed here. Hint: in the narrow section the water must have 4 times the velocity as in the wide section. I'm off for now but maybe others can pick up if you need additional help.
 
Let me see if I have the equation correct.

P1-P2=1/2 (density) (V2^2-V1^2)

and

A1V1=A2V2

Is this what you are talking about?
 
Yes. Those are correct. You can see the derivation here -

http://en.wikipedia.org/wiki/Bernoulli's_principle
 
Thanks for your help this make sense now
 

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