1. Engineering
  2. Other
  3. a high flying fountain is required for decoration and air...

Question: a high flying fountain is required for decoration and air...

Question details

A high flying fountain is required for decoration and air conditioning purpose for a high building.  The fountain consists of a concrete tank in which a submersible pump is installed.  Water is then pumped to a height L2, and diverted in another pipe section L1 at an angle LaTeX: \alphaα outwards through a nozzle as shown in Figure 1.  For easier design decision, the angle LaTeX: \alphaα  is fixed at 30 degrees.

 

You are required to design the system using one of the three pumps: 75/35, 75/56, 115/576.  The pump characteristics are shown in Figure 2.

 

Selection criteria for system performance:

  1. Must be one of the designated pumps
  2. Height of fountain above ground to be maintained between 15 m to 20 m
  3. Larger water flowrate preferred. More water gives a better impression of the fountain

Which set of system design parameters would you suggest?

Formulae applicable to this question:

Pressure drop in a pipe is given by:

Δ P = P 1 P 2 = 128 μ L Q π D 4

where

  • P1 = upstream fluid pressure (N/m2)
  • P2 = downstream fluid pressure (N/m2)
  • L = length of pipe section (m)
  • Q = fluid mass flowrate (kg/s)
  • LaTeX: \piπ = circle constant = 3.14159
  • LaTeX: \muμ  = dynamic viscosity of water at operating temperature = 0.29
  • D = internal diameter of the pipe

Pressure drop through pipe bend is given by:

Δ P = P 1 P 2 = 1 2 f s ρ v 2 π R b D θ 180 o + 1 2 k b ρ v 2

where P1, P2, D and LaTeX: \piπ   have the same meaning as before.

  • Rb = bend radius
  • v = velocity of fluid flow at the centre line of the bend.
  • LaTeX: \rhoρ  = the density of water (very heavily salted mineral water) (= 1,029 kg/m3)
  • LaTeX: \thetaθ  = the angle of circular segment of the bend sustained from the centre of bend in degrees

The pipe flow factor kb depends on the angle of bend. The value of kb can be interpolated from Table 1 and 2:

Table 1:  kb values for 90 degrees bends

Rb/D

0.5

0.6

0.7

0.8

1.0

2.0

3.0

4.0

5.0

6.0

8.0

10.0

kb

0.85

0.68

0.56

0.48

0.39

0.24

0.18

0.16

0.15

0.14

0.13

0.13

Note: For Rb/D > 10.0, kb = constant = 0.13.

Table 2:  kb values for 120 degrees bends

Rb/D

0.5

0.6

0.7

0.8

1.0

2.0

3.0

4.0

5.0

6.0

8.0

10.0

kb

0.95

0.74

0.60

0.53

0.44

0.26

0.26

0.18

0.16

0.15

0.15

0.15

Note: For Rb/D > 10.0, kb = constant = 0.13.

The coefficient of pipe bend friction LaTeX: f_sf s depends on Reynolds number Re.  Reynolds number is given by:

R e = ρ v D μ

If Re < 2300, then it is laminar flow,

f s = 64 R e

If Re > 4000, then it is turbulent flow,

1 f s = 2 log 10 ( ϵ 3.7 D + 2.51 R e f s )

Stainless steel will be used throughout the system.  The pipe material roughness factor LaTeX: \epsilonϵ = 0.0015.

If 2300 < Re < 4000, then it is critical flow.  Interpolate between laminar and turbulent flows using Re value.

 

Group of answer choices

L1 = Nozzle section pipe length = 1 m

L2 = Rising section pipe length = 15 m

L3 = Horizontal istance of fountain from the nozzle = 15 m

d1 = Pipe diameter = 30 mm

dn = Nozzle outlet diameter = 10 mm

Rb = Bend radius = 0.1 m

L1 = Nozzle section pipe length = 4 m

L2 = Rising section pipe length = 13 m

L3 = Horizontal istance of fountain from the nozzle = 15 m

d1 = Pipe diameter = 40 mm

dn = Nozzle outlet diameter = 5 mm

Rb = Bend radius = 1 m

L1 = Nozzle section pipe length = 9 m

L2 = Rising section pipe length = 10 m

L3 = Horizontal istance of fountain from the nozzle = 15 m

d1 = Pipe diameter = 125 mm

dn = Nozzle outlet diameter = 12 mm

Rb = Bend radius = 1 m

L1 = Nozzle section pipe length = 5 m

L2 = Rising section pipe length = 20 m

L3 = Horizontal istance of fountain from the nozzle = 15 m

d1 = Pipe diameter = 30 mm

dn = Nozzle outlet diameter = 5 mm

Rb = Bend radius = 0.1 m

L1 = Nozzle section pipe length = 0.5 m

L2 = Rising section pipe length = 14 m

L3 = Horizontal istance of fountain from the nozzle = 15 m

d1 = Pipe diameter = 40 mm

dn = Nozzle outlet diameter = 10 mm

Rb = Bend radius = 0.1 m

L1 = Nozzle section pipe length = 1 m

L2 = Rising section pipe length = 19 m

L3 = Horizontal istance of fountain from the nozzle = 15 m

d1 = Pipe diameter = 40 mm

dn = Nozzle outlet diameter = 10 mm

Rb = Bend radius = 0.5 m

 

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution