Question

In a section of horizontal pipe with a diameter of 3.00 cm the pressure is 100 kPa and water is flowing with a speed of 1.50 m/s. The pipe narrows to 2.00 cm. What is the pressure in the narrower region?

Answer: ________ kPa

Answer 1

continuity equation:
\[A_1v_1=A_2v_2\]\[\pi \frac{ d_1^2 }{ 4 }v1=\pi \frac{ d_2^2 }{ 4 }v_2\]
\[v_2=\frac{ d_1^2 }{ d_2^2 }v_1\]
and Bernoulli equation:
\[p_1 +\frac{ 1 }{ 2 }\rho_{water}v_1^2=p_2+\frac{ 1 }{ 2 }\rho_{water}v_2^2\]
solve for p2

Answer 2

99,54 kPa

Answer 3

\[p _{2}= \frac{ p _{1}v _{1^{2}} }{ v _{2^{2}} }\]

Answer 4

I dont think i have the equation right, because i am pretty sure the answer is 95.4, but i cant figure out how to get that

Answer 5

oh , I made the mistake I chose 100 as density not 1000 as it should be I redo it and find 95,429 kPa

Answer 6

\[p_2=p_1-\frac{ 1 }{ 2}\rho_{water}v_1^2[1-\left( \frac{ d_1 }{ d_2 } \right)^4]\]

Answer 7

sorry it sholud be p1 + the rest

Answer 8

so p2= 100 000 +500*2,25[1-5,0635]

Answer 9

and then convert to kPa by dividing solution by 1000

Answer 10

wait, i didnt get that, can you show me what you plugged into p2=p1−12ρwaterv21[1−(d1d2)4]

Answer 11

\[p _{2}= (1000)+ .5 (1000)(1.5)^{2}(1-(3/4)^{4})\]

Answer 12

mean (3/2)^4

Answer 13

yes

Answer 14

that's correct

Answer 15

how come i get like -3570.31

Answer 16

oh 100 kPa =100 000 Pa instead of 1000 put 100 000

Answer 17

ok