Water is flowing through a 0.05 m diameter pipe from a large reservoir, as shown
ID: 1822668 • Letter: W
Question
Water is flowing through a 0.05 m diameter pipe from a large reservoir, as shown.The water level in the reservoir is 25 m above the horizontal pipe segment at the exit
from the tank. The pipe initially is bent down and later up, emerging above the ground
level. The loss coefficient in the three elbows is K = 0.25, and we can assume a Darcy
friction coefficient of f = 0.02. Also for water ? = 1000 kg/m3, µ = 10-3 N s/m2 .
(a) Calculate the average discharge velocity and the Reynolds number in the pipe, and (b)
Calculate the height h of the water fountain above the end of the pipe.
Here is a link with the picture: http://s1077.photobucket.com/albums/w462/portland36/?action=view¤t=EM340HW71.jpg
Explanation / Answer
(a).
Water is flowing through a 0.05 m diameter pipe from a large reservoir. The water level in the reservoir is 25 m above the horizontal pipe segment at the exit from the tank.
calculation of discharge velocity at the end point of the pipe (where fountain starts) :
According to Bernoulli's Equation ,
P1/g + v12/2g + z1 = P2/g + v22/2g + z2 + head losses
here, atmoshepheric pressure can be assumed. (i.e. P1=P2)
and v1 =0 m/s (this is the velocity of water at the surface of reservoir)
assume reference line as opening pipe from the reservoir.
therefore, z2 = 25 m -1m = 24 m
head losses = head loss due to pipe friction + head loss due to elbows
calculation of head loss due to pipe friction :
according to Darcy-Weisbach equation,
head loss, hf = flv2/(d*2*g)
where, L = length of pipe
f = friction coefficient.
d = dia of pipe.
Given:
dia of pipe = 0.05 m
length of pipe from the diagram = 100+2 = 102 m
f= 0.02
therefore, head loss due to pipe friction, hf = 0.02*102*v22/(0.05*2*9.81)
hf = 2.0795 v22 m
calculation of head loss due to elbows :
head loss due to elbows (3 elbows given in diagram)= 3*(Kv2/2g) = 3(0.25*v22/(2*9.81)) = 0.0382 v22 m
therefore, total head loss = 2.0795 v22 + 0.0382 v22 = 2.1177 v22 m
put the all values in the above Bernoulli's equation, we get ;
0+ 0+ 24 = 0 + v22/2*9.81 + 0 + 2.1177 v22
by solving this equation , we get ;
v2 = 3.327 m/s
hence, the discharge velocity in the pipe = 3.327 m/s
Reynolds number in the pipe, Re = vD/
where, v = discharge velocity.
D is the dia of pipe
= kinematic velocity
therefore, Re = 1000*3.327*0.05/10-3
= 166350
hence, Reynolds number of flow in the pipe = 166350
(b).
calculation of the height,'h' of the water fountain above the end of the pipe :
it is calculated by simply energy conservation theorem,
kinetic energy of flow = potential energy
because at the tip of the flow from the fountain, velocity of flow is 0.
therefore,
(1/2)**v2 = gh
h = v2/2g = 3.3272/2*9.81 = 0.564 m
hence, the height of the water fountain above the end of the pipe = 0.564 m
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.