Problem 6: Pipe The water enters the two-story building through a horizontal pip
ID: 1545933 • Letter: P
Question
Problem 6: Pipe
The water enters the two-story building through a horizontal pipe with an inner diameter 4 cm and the
pressure of 10 atm. The velocity of the water flow in the pipe is 5 m/s. The horizontal pipe is connected
to a vertical pipe which leads to bathrooms in each story.
a) What is the velocity of the water flow in the vertical pipe
if the radius of the pipe is 2 cm.
b) What is the pressure in the pipe in the first story (point
A)? The vertical distance from the horizontal pipe is 2 m.
c) What is the percentage drop of the pressure in the second
story (point B) from the first story (point A) if the height
of the story is 3 m.
Explanation / Answer
a)
To find the velocity of the water in the vertical pipe, we use the equation of continuity: A*v =constant
where A= area of the pipe, v=velocity of the water.
Hence we write : A H * VH = A V * V V
A H = area of horizontal pipe
VH = velocity in the horizontal pipe
A V = area of vertical pipe
VV = velocity in the vertical pipe
The area of the horizontal and the vertical pipe is the same (because their radius are same i.e. 2cm)
This means that VH = VV = 5m/s
b)
For calculating pressure, we use Bernoulli's principle:
P+ gh +v2/2 = constant
P = pressure, = density of the fluid (water in our case), h = height of the point of interest from the origin
v= speed of the fluid at the point of interest
FOR A
v=5m/s, h=2m, P=P (to be calculated)
FOR HORIZONTAL PIPE LEVEL
v=5m/s, h=0m, P=10 atm
Using the principle at these two points we get
P+*10*2 = 10 atm + *g*0 (the velocity terms on both sides have cancelled out)
Density of water is 1000 kg/m3
This gives P= 993250 Pa ( i have converted 1 atm = 101325 Pa. Pa is the SI unit of pressure.)
Similarly by using h=5m , we can find pressure ( P' ) at point B
P' = 963250 Pa
Percentage drop in pressure = (P-P')/P *100 = 3.02%