By Ahmad Suhendra
The saddles are designed to support the weight of the penstock full of water, but not to resist significant longitudinal forces. The vertical component of the weight to be supported, in kN, has a value of :
F1 = (Wp + Ww) * L Cos θwhere :
Wp = weight of pipe per meter (kN/m)
Ww = weight of water per meter of pipe (kN/m)
L = length of pipe between mid points of each span (m)
θ = Angle of pipe with horizontal
The design of support rings is based on the elastic theory of thin cylindrical shells. The pipe shell is subject to beam and hoop stresses, and the loads are transmitted to the support ring by shear. If penstocks are continuously supported at a number of points, the bending moment at any point of penstock may be calculated assuming that it is a continuous beam, and using the corresponding equation. The rings are welded to the pipe shell with two full length fillet welds and are tied together with diaphragm plates.
The span between supports L is determined by the value of the maximum permissible deflection L/65000. Therefore the maximum length between supports is given by the equation:
L= 182.61 * [(Dp + 0.0147)^4 - Dp^4)]^(1/3) / (Wp + Ww)
Example :
What is The vertical component of the weight to be supported if such data is given below:
1.Diameter of pipe (Dp) = 0.636 m
2.Pipe thickness (e) = 0.005 m (5 mm)
3.Density of pipe (ρ steel) =7.9 ton/m^3
4.Density of water (ρ water) = 1 ton/m^3
5.Angle of pipe with horizontal (θ )= 5 deg
I. Wp (weight of pipe per meter)
= phi * ( Dp + e) * e * ρ steel
= 3.14 (0.636 + 0.005)* 0.005 * 7.9
= 0.079 ton/m
II. Ww (weight of water per meter of pipe)
= [(phi x ( Dp^2) / 4] * ρ water
= [(3.14 x 0.636^2)/4] * 1
= 0.32 ton /m
III. Total weight (Wp + Ww)
= 0.399 ton/m (Wtotal)
= 0.399 * 9.81
= 3.914 kN/m
IV. The maximum length between supports.
L= 182.61 * [(Dp + 0.0147)^4 - Dp^4)]^(1/3) / (Wp + Ww)
= 182.61 * [(0.636 + 0.0147)^4 - 0.636^4]^(1/3) / (3.914)
= 182.61 * [0. 01566 ]^(1/3) / (3.914)
= 182.61 *[0.2502]/3.914
= 11.67 m
V. The vertical component of the weight to be supported.
F1 = (Wp + Ww) * L Cos θ
=3.914 kN/m * 11.67 m* Cos 5
= 45.503 kN
Ref :
ESHA (European Small Hydropower Association),”Layman’s Handbook on How To Develop a Small Hydro Site,”2nd ed, 1998 http://www.scribd.com/doc/8885765/Layman-Handbook-for-hydro-electric-power-plants
Photo
http://www.fr.aps-sales.com/documentos/downloads/HydroPower%20and%20penstock%20applications.pdf
