KuDos® Hydraulic Power Puncher PNST-10

Equivalent Hydraulic Diameter

The hydraulic diameter - d_h - is used to calculate the dimensionless Reynolds Number to determine if a flow is turbulent or laminar. A flow is

• laminar if Re < 2300
• transient for 2300 < Re < 4000
• turbulent if Re > 4000

The hydraulic diameter is also used to calculate the pressure loss in a ducts or pipe.

The hydraulic diameter is not the same as the geometrical diameter in a non-circular duct or pipe and can be calculated with the generic equation

d_h = 4 A / p (1)

where

d_h = hydraulic diameter (m, ft)

A = area section of the duct (m², ft²)

p = wetted perimeter of the duct (m, ft)

Note! Inches are commonly used in the Imperial unit system.

Hydraulic Diameter of a Circular Tube or Duct

Based on equation (1) the hydraulic diameter of a circular duct can be expressed as:

d_h = 4 π r² / 2 π r

= 2 r (2)

where

r = pipe or duct radius (m, ft)

As we could expect the hydraulic diameter of a standard circular tube or duct is two times the radius.

Hydraulic Diameter of a Circular Tube with an inside Circular Tube

Based on equation (1) the hydraulic diameter of a circular duct or tube with an inside duct or tube can be expressed as

d_h = 4 (π r_o² - π r_i²) / (2 π r_o + 2 π r_i)

= 2 (r_o - r_i) (3)

where

r_o = inside radius of the outside tube (m, ft)

r_i = outside radius of the inside tube (m, ft)

Hydraulic Diameter of Rectangular Tubes or Ducts

Based on equation (1) the hydraulic diameter of a rectangular duct or pipe can be calculated as

d_h = 4 a b / (2 (a + b))

= 2 a b / (a + b) (4)

where

a = width/height of the duct (m, ft)

b = height/width of the duct (m, ft)

Hydraulic Diameter

Flow Rate and Hydraulic Diameter

The chart above shows the relationship between flow rate and hydraulic diameter for three airless spray orifices with 24" spray patterns. The data shown are for a 1225, 1231 and 1239 spray tip respectively. The flow rates are for water at 20.15°C and 2000 psi.

You will notice that the hydraulic diameter measures noticeably less than the rated orifice size. This is discussed on the Cv Value page.

The slope of this curve fit is specific to the basic geometry of the spray orifice. In other words, spray tips with a different "V" angle, but similar hydraulic diameter will produce a different curve fit slope. Therefore, spray tips that are scaled one size to the next with similar ratios (i.e. Aspect Ratio) will follow a given trend.

It is the change in "V" angle that affects the aspect ratio of the orifice. In this case, the included "V" angle for a these 12XX spray tips is approximately 26.6° to 26.8°.

The included "V" angle of 1221 and 1223 spray tips is approximately 23.7° to 24.2°. The 1221 and 1223 would produce a different sensitivity relationship between flow rate and hydraulic diameter.