Question

A water pipe having a 2.55 cm inside diameter carries water into the basement of a house at a speed of 0.760 m/s and a pressure of 237 kPa. If the pipe tapers to 1.56 cm and rises to the second floor 6.04 m above the input point, what are the (a) speed and (b) water pressure at the second floor?

Answer 1

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A water pipe having a 2.5 cm inside diameter carries water into the basement of a house at a speed of 0.91 m/s and a pressure of 165 kPa. The pipe tapers to 1.4 cm and rises to the second floor 7.3 m above the input point.


(a) What is the speed at the second floor?

(b) What is the water pressure at the second floor?   

Data:

Height of the 2nd floor, h = h2 - h1 = 7.3 m

Pressure at the base, P1 = 165 x 10^3 Pa

Velocity at the base, v1 = 0.91 m/s

Diameter of the pipe at the base, D1 = 2.5 x 10^-2 m

Diameter of the pipe at the top, D2 = 1.4 x 10^-2 m

Density of water, ? = 1000 kg/m^3

Solution:

(a)

From the equation of continuity,

A1 v1 = A2 v2

? r1^2 v1 = ? r2^2 v2

r1^2 v1 = r2^2 v2

D1^2 v1 = D2^2 v2

v2 = ( D1 / D2 )^2 * v1

     = ( 2.5 / 1.4 )^2 * 0.91

     = 2.9 m/s

Ans:

Velocity at the 2nd floor, v2 = 2.9 m/s (b)

From the Bernoulli's equation,

P1 / ? + ( v1^2 / 2 ) + g h1 = P2 / ? + (v2^2 / 2 ) + g h2

(P1 - P2 ) / ? = [ ( v2^2 - v1^2 ) / 2 ] + g ( h2 - h1 )

(P1 - P2 ) / ? ={ [ (2.9)^2 - (0.91)^2 ] / 2 } + ( 9.8 * 7.3 )

                        = 75.33

P1 - P2 = 75.33 x 10^3

P2 = 165 x 10^3 - 75.33 x 10^3

      = 89.67 x 10^3 Pa

      = 89.67 kPa

Ans:

Pressure at the 2nd floor, P2 = 89.67 kPa