Page 97 - Industrial Ventilation Design Guidebook

62 CHAPTER 4 PHYSICAL FUNDAMENTALS

When k = 0.03 mm, the ratio k/d — 0.000 375, and therefore the friction
5
factor £ 01 = 0.0193. Correspondingly, Re 13 = 10 xlO and £ 13 = 0.0196.
The formula for pressure loss is

The dimensioning of pipe 3-4 happens by means of Eqs. (4.68) and (4.70).
The iteration equation is now

Calculations are dealt with in the following stages

1. d 4 is chosen.
2. Re and k/d 4 are calculated.
3. £ 54 is read from the Moody chart as a function of Re and k/d 4_
4. A new d 4 is calculated with Eq. (4.71) until the d 4 value is
suitable.
Calculations are best carried out in a tabular form. The value of d 4 is 29.7 mm.
In practice the next larger standard pipe size would be selected.
The diameter d 2 is solved analogously. The Bernoulli equation at the in-
terval 1-2 is

Example 4
A pump lifts water from a lake. At the pump suction entry a foot valve is
fitted. Determine the maximum static delivery height the water can be raised
without cavitation taking place. The saturation pressure of water is 1.23 kPa
3 1 1
at 10 °C and the dynamic viscosity is 1.3 x 10~ kg nr s" . The suction pipe
1
water velocity is 2.0 m s" , the internal pipe diameter is 100 mm, and the pipe
roughness is 0.03 mm. The resistance of the foot valve is 4.5.
Note: Cavitation occurs when the pressure at a point in a liquid flow
field is equal or less than the vapor pressure of the liquid. At this point
bubbles of vapor are formed, this is cavitation. It has serious effects such