In an industrial cooling process, water is circulated through a system. If the water is pumped with a speed of 0.45 m/s under a pressure of 400 torr from the first floor through a 6.0-cm diameter pipe, what will be the pressure on the next floor 4.0 m above in a pipe with a diameter of 2.0 cm?

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## Answers ( 6 )

Hey sorry for taking so long to get back to you, I tried workingit out yesterday and I couldn't get the bernoulli equation to comeout right because I used the wrong relation between area andvelocity. They have the following realtion:

Now use the bernoulli equation..

Put all units ----in SI systemIn an industrial cooling process, water is circulated through asystem.

If the water is pumped with a speed of(

v)_{1}= 0.45 m/sunder a pressure of (

P) from the first floor througha(_{1}= 400 torrD) diameter pipe,_{1}= 6.0cmLet '

Pbe the pressure on the next floor (_{2}'h = 4.0 m) above in a pipe with adiameter of ( D_{2}= 2.0 cm)Density of water ( ? ) = 1000 kg / m^{3}From the equation of continuity wehaveThe Flow rateis A

_{1}v_{1}=A_{2}v_{2}0r, v_{2}= A_{1}v_{1}/ A_{2}Or,v_{2}= ( D_{1}/ D_{2})^{2}v_{1}Apply ; Bernoulli's Theorem

P_{1}+ ( 1/2 )*?* v

Put the above givenvalues in the above expression , to get_{1}^{2}+ 0 = P_{2}+ ( 1/2 )* ? * v_{2}^{2}+ ? * h * g' P

_{2}'http://en.wikipedia.org/wiki/Bernoulli%27s_principle#Incompressible_flow_equation

0.5(v squared) + gh + P/r = 0.5(v squared) + gh + p/r

the left side is for the first floor where

(v squared) is (o.45 squared) and g is 9.8 but h is zero

and P is given as 400torr which must be converted to pascals

and r, the density of water is 1g per ml, you have to convert it tokg per cubic meter or either do some algebra and divide it out ofthe equation.

right side

calculate velocity. area x vel on the little pipe equals area xvel

on the big pipe. area is pi x r x r. pi is 3.14 and r isdiameter/2. convert the diameter from cm to meters and find areathen find velocity for the right side.

centimeters x 1meter/(100 cm)= meters

6cm=o.06 meters

radius on left is 0.03meters

area on left is 3.14 x 0.03 x 0.03

area x vel on left is

3.14(0.03 squared)(0.45)=3.14(0.01 squared)(veloc upstair)

calculate your velocity upstairs and put it in the right side ofthe bernoulli equation. h is 4 meters for the right side of thebernouli

http://www.onlineconversion.com/density_common.htm

this is how you convert grams per ml into kg per cubic meters

just mult by 1000. the density, r, of water is 1 gram per ml

Source:http://au.answers.yahoo.com/question/index?qid=20080203121146AAHwdwX

"In an industrial cooling process, water is circulated through asystem. If the water is pumped with a speed of 0.45 m/s under apressure of 400 torr from the first floor through a 6.0-cm diameterpipe, what will be the pressure on the next floor 4.0 m above in apipe with a diameter of 2.0 cm?"

thanksYou will need the velocity of the fluid in the pipe for the 6 cmcase.

Now use the fluid/energy equation..