Water enters a house through a pipe with a dia of 2cm at an abs pressure of 4atm. A 1 cm pipe leads to a secon

Question

Water enters a house through a pipe with a dia of 2cm at an abs pressure of 4atm. A 1 cm pipe leads to a second floor bathroom 5m above .When the flow speed at the inlet pipe is 1.5 m/s. What is the flow speed, the pressue and volume flow rate in the bathroom

Answer 1

First, you have conservation of mass, so Q in = Q out.

Therefore you have to find the Area of the 2 cm pipe. Units must match. Area = 0.02^2*pi/4 = 0.000314 M^2.

Q = V*A = 1.5 M/s * 0.000314 M^2 = 0.000471 M^3/s

Then, Qin = Q out, so Qout = V' * A',
so V'=Q/A' = 0.000471M^3/s / 0.01^2*pi/4 M^2= 6 M/s

The Pressure Head is reduced by the amount of elevation and exit velocity.

The flow rate is the same, or Q = 0.000471 M^3/s.

Answer 2

You have to use Bernoulli's equation to get the pressure before the exit, provided there is no other branch from the main header.

If you consider the entry level as datum, the static head on the LHS becomes zero, pressure is 4 bara and velocity is 1.5m/s.

On the RHS, pressure is unknown, velocity is 6m/s and elevation is 5m. Convert pressure and velocity into pressure head and velocity heads respectively. You should get about 3.33 bara.

Answer 3

v = 1.5*(2/1)^2 = 6 m/sec
P = 1 atmosphere, by definition
V =Av =PI*(6 m/s)(100cm/m)/4 = 471 cc/s, or 0.471 l/s

(the 5m difference in elevation has insufficient effect on air pressure, which is the determining factor for exit pressure.)