Question

Oil is flowing through a horizontal pipe constriction. In the large section, the pipe has a diameter of 1.7 meters and a pressure of 500 kPa. If the pipe constricts to a diameter of 0.5 meters, what is the pressure in the constricted pipe section. (Assume the oil flow rate is 65 m3/min and oil density is 900 kg/m3)

		49,432.419 kPa
		13.096115 kPa
		486.403885 kPa
		513.801133 kPa

2. Oil is flowing through a horizontal pipe expansion. In the small section, the pipe has a diameter of 0.8 meters and a pressure of 700 kPa. If the pipe expands to a diameter of 1.5 meters, what is the pressure in the expanded pipe section. (Assume the oil flow rate is 65 m3/min and oil density is 900 kg/m3)

		701.921125 kPa
		697.740637 kPa
		2.621125 kPa
		7,616.05127 kPa

Answer 1

4th Option 7,616.05127 kPa is the correct answer.

let
d1 = 0.8 m
P1 = 700 kPa
Volume flow rate, dV/dt = 65 m^3/s
rho = 900 kg/m^3
d2 = 1.5 m
P2 = ?

let v1 and v2 are the speeds of oil at the two locations.

we know, dV/dt = A1*v1

v1 = (dV/dt)/A1

= (dV/dt)/(pi*d1^2/4)

= 65/(pi*0.8^2/4)

= 129.31 m/s

we know, dV/dt = A2*v2

v2 = (dV/dt)/A2

= (dV/dt)/(pi*d2^2/4)

= 65/(pi*1.5^2/4)

= 36.782 m/s

now use Bernoulli's equation

P1 + (1/2)*rho*v1^2 = P2 + (1/2)*rho*v2^2

==> P2 = P1 + (1/2)*rho*(v1^2 - v2^2)

= 700*10^3 + (1/2)*900*(129.31^2 - 36.782^2)

= 7616 kPa