Homework SourseWater flowing in a horizontal pipe is at a pressure of 155 x
Water flowing in a horizontal pipe is at a pressure of 1.55 x 105 Pa at a point where its cross-sectional area is 2.00 m2. When the pipe narrows to 0.400 m2, the pressure drops to 1.16 x 105 Pa.
(a) Find the water\'s speed in the wider pipe (m/s).
(b) Find the water\'s speed in the narrower pipe (m/s).
Solution
Pressure difference P = P1 - P2
= (1.55 - 1.16)*10^5 Pa
= 0.39*10^5 Pa
Density of water = 1000 Kg/m^3
Cross-sectional area of wider pipe A1 = 2 m^2
Cross-sectional area of narrow pipe A2 = 0.4 m^2
Let v1 and v2 are the speed of water at wider and narrow pipes respectively.
From equation of continuity
A1 v1 = A2 v2
v2 = (A1/A2) * v1
= (2 m^2/0.4 m^2) * v1
= 5 v1 -------------[1]
From Bernouli equation we can write:
P = (1/2)[v2^2 - v1^2]
0.39*10^5 Pa = 0.5 * (1000 Kg/m^3) [(5 v1)^2 - v1^2]
24 v1^2 = 78
v1^2 = 3.25
v1 = 1.802 m/s
(a)
The water\'s speed in the wider pipe v1 = 1.802 m/s
(b)
The water\'s speed in the narrow pipe v2 = 5 v1 (from equation [1])
= 5 * 1.802 m/s
= 9.01 m/s
