# In an industrial cooling process, water is circula...

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?

1. 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:

Then you can solve for V2, or the velocity of the pip with a2.0 cm diameter

Now use the bernoulli equation..
You will want
And now you are looking for the Pressure of the second fluidso your equation is
Solving for the pressure Px gives you:
2. Put all units ----in SI system
In an industrial cooling process, water is circulated through asystem.
If the water is pumped with a speed of( v1 = 0.45 m/s)
under a pressure of ( P1 = 400 torr) from the first floor througha( D1 = 6.0cm) diameter pipe,
Let ' P2 ' be the pressure on the next floor ( h = 4.0 m ) above in a pipe with adiameter of ( D2 = 2.0 cm)
Density of water ( ? ) = 1000  kg / m3
From the equation of continuity wehave
The Flow rateis          A1 v1 =A2v2

0r,                v2 = A1 v1/ A 2

Or,              v2= ( D1 / D2 ) 2 v1

Apply ; Bernoulli's Theorem
P 1 + ( 1/2 )*?
* v 1 2 + 0   =    P2+ ( 1/2 )* ? * v22 + ? * h * g
Put the above givenvalues in the above expression , to get
' P2 '

3. 45.6
4. use the bernoulli equation from your book or get it from the webpage
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
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

5. Whenever you have time could you please finish the answer youstarted on the question,

"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?"
thanks
6. You will need bernoullies equation for this one.
As well as the area/velocity relation

You will need the velocity of the fluid in the pipe for the 6 cmcase.
A2 =0.00282 m^2
A1 = .000314m^2
V 1 = 1.8m/s

Now use the fluid/energy equation..