Water is flowing through a pipe that slowly gets smaller as it rises to the bath

Question

  Water is flowing through a pipe that slowly gets smaller as it rises to the bathroom on your second floor (10 m high). The pipe coming into your house is 3 cm in diameter, the pressure there is 3x105 Pa, and the water is moving at .8 m/s. The diameter of the pipe in the upstairs bathroom is 1.5 cm. How fast is the water moving right before it leaves the pipe in the bathroom?0.2 m/s0.4 m/s1.6 m/s3.2 m/s What is the pressure of the water in the pipe right before it leaves the pipe?1.50x105 Pa1.97x105 Pa2.88x105 Pa3.67x105 PaFluids and I don't get along so I know I'm making this harder than it needs to be. Any help would be great!

Explanation / Answer

By equation of continuity,

A1v1=A2v2

v2=v1*(A1/A2)=0.8*(3^2/1.5^2)=3.2m/s

P1+0.5*rho*v1^2=P2+0.5*rho*v2^2+rho*gh

P2=P1+0.5*rho*v1^2-0.5*rho*v2^2-rho*gh=3*10^5+0.5*1000*0.8^2-0.5*1000*3.2^2-1000*9.8*10

=1.97*10^5Pa

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