Water at a pressure of 3.8 atm at street level flows into an office building at
ID: 2262614 • Letter: W
Question
Water at a pressure of 3.8 atm at street level flows into an office building at a speed of 0.4 m/s through a pipe 5.6 cm in diameter. The pipes taper down to 2.4 cm in diameter by the top floor, 30 m above. Calculate the water pressure in such a pipe on the top floor.(g = 9.8 m/s2) Pa
Water at a pressure of 3.8 atm at street level flows into an office building at a speed of 0.4 m/s through a pipe 5.6 cm in diameter. The pipes taper down to 2.4 cm in diameter by the top floor, 30 m above. Calculate the water pressure in such a pipe on the top floor.(g = 9.8 m/s2) Pa
Explanation / Answer
p1 + ?gh1 + ?/2*v1^2 = p2 + ?gh2 + ?/2*v2^2
where the left side is the total pressure at street level.
v1 = velocity in large tube
v2 = velocity in small tube = v1*5.6^2/2.4^2 =2.18m/s
h1 = street level, h2 = -30 m because the hydrostatic pressure reduces with height.
? = density = 1000 kg/m^3
p = static pressure
?/2*v^2 = kinetic pressure
3.8*1.013*10^5 N/m^2 + 500*0.4^2 = p2 -1000*9.8*30 + 500*1.7 ^2
p2 = 92465 N/m^2 = 0.925 atm
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