• Journal of Korea Water Resources Association
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• v.30 no.5
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• pp.495-501
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• 1997

Pumping power being given, traditional method requires an iteration process for the solution of discharge and pipe diameter. Yoo and Kang (1996) have developed explicit equations for the estimation of discharge and pipe diameter for the cases of uniformly rough pipe on a sloping bed with a pumping power. The use of poser law for the estimation of friction factor enabled to develop the explicit form of equations. Yoo (1995a) has suggested the mean friction factor method for the estimation of friction factor of commercial pipe or composite surface pipe. With the same approach, the present work has developed the explicit equations of discharge or pipe diameter for the general case of commercial pipe on a sloping bed with a pumping power by adopting the mean friction factor method.

• Journal of Korea Water Resources Association
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• v.38 no.7 s.156
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• pp.527-535
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• 2005

The computation of normal depth is very important for the design of channel and the analysis of water flow. Drainage pipe generally has the shape of curvature like circular or U-type, which is different from artificial triangular or rectangular channel. In this case, the computation of normal depth or the derivation of equations is very difficult because the change of hydraulic radius and area versus depth is not simple. If the ratio of the area to the diameter, or the hydraulic radius to the diameter of pipe is expressed as the water depth to the diameter of pipe by power law, however, the process of computing normal depth becomes relatively simple, and explicit equations can be obtained. In the present study, developed are the explicit normal depth equations for circular and U-type pipes, and the normal depth equation associated with Hagen (Manning) equation and friction factor equation of smooth turbulent flow by power law is also proposed because of its wide usage in engineering design.

• Journal of Korea Water Resources Association
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• v.32 no.1
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• pp.31-40
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• 1999

After investigating the basic problems of seepage flow, the friction factor equation of power form was developed for solving them. The use of power law for the estimation on friction factor enabled to develop the explicit form of equations without any iteration process being related to various non-dimensional physical numbers. For the derivation of friction factor equations, the existing data were re-analyzed, and the simple method of seepage flow design was devised with the power law equations for the estimation of slope, discharge, and diameter.

• Water for future
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• v.29 no.3
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• pp.163-176
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• 1996

When a pipe is deployed on a sloping bed, pumping power required for a discharge can be estimated immediately without any iteration process with an explicit form of a friction factor equation. Pumping power being given, however, traditional method requires an iteration process for the solution of discharge and pipe diameter even for the uniformly-rough pipe. You (1955b) has suggested explicit equations for the estimation of discharge and pipe diameter particularly for the cases of pipe on a slopintg bed without pumping and pipe on a horizontal bed with a pumping power. Based on his approach and previous results, the present researchers have developed explicit equations of discharge and pipe diameter for the general case of pipe on a sloping bed with a pumping power. The equations of boundary criteria are also presented in explicit way which render proper choice of various equations suitable for the flow condition between five characteristics. Verification studies are also carried out by applying the explicit equations to a practical example.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.3
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• pp.202-208
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• 2001

Explicit approximation has been developed to estimate the run-up height on S-berm breakwater on the basis of Saville's hypothetical slope method. For the explicit expression of run-up height several relations are developed to represent the ratio of run-up height against breakwater slope with various conditions of water depth and wave steepness. For the verification of explicit approximation the results are compared with Saville's measurement data and simple expression of Delft Hydraulic Laboratory.

• Journal of Korea Water Resources Association
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• v.34 no.1
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• pp.31-43
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• 2001

The friction factor of commercial pipe varies with wide range depending on pipe type and pipe size. Various methods can describe the wide variation of friction factor with good accuracy, but they normally require an iteration process even for solution of a simple case. Power law can result in an explicit form of solver so that the power law is rigorously employed for the development of direct solution technique. The parameters used in the present form of power law are allowed to haute some variation with pipe size and Reynolds number as well as pipe type for wider coverage with good accuracy, while Hazen-Williams equation permits limited variation which accounts only for the roughness or the pipe type. Furthermore secondary loss is considered in the development of explicit equations for design of commercial pipes.

• Water for future
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• v.28 no.5
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• pp.175-189
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• 1995

Pipe design normally requires pump power, discharge rate or pipe diameter for each condition given. Due to several investigators the pipe friction factor can now be estimated by explicit way when the flow condition is provided. In various problems of pipe design, however, the flow condition cannot be pre-determined even for the uniformly rough pipe. In these cases a lot of iterations are often required to have an accurate solution with ordinary approach. This paper presents the explicit way of estimating the discharge rate and pipe diameter without any iteration process being related to non-dimensional physical numbers, power-diameter number, power-discharge number, and discharge-slope number, which enable to develop explicit forms of equations.

• Journal of Korea Water Resources Association
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• v.32 no.4
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• pp.469-478
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• 1999

Explicit equations of minimum velocity, energy slope and pipe diameter are developed to ensure the cleaning of sewerage pipes. The equations of power form are employed for the estimation of critical shear stress of sediment particles and the friction factor of commercial pipes. They are all based on the existing laboratory data. Several cases are tested to check the values suggested in the manual, using the equations developed in the present study.

• Journal of Korea Water Resources Association
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• v.31 no.5
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• pp.565-574
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• 1998

The friction factor distribution of commercial pipes vary according to the pipe type and size. The present paper developed the friction factor equations of power law by analyzing the data reported by Colebrook(1938). Generally, pipe design requires pump power, discharge or pipe diameter for each condition given. Yoo(1995b) has suggested the basic equations for the explicit design of uniformly rough pipe and Yoo and Kang(1996) have refined those equations for the cases of uniformly rough pipe on a sloping bed with a pumping power. Furthermore Yoo and Kang(1997) have studied the design of commercial pipe for a general case. The approach gives relatively accurate solutions, but the equations obtained are rather complicated. In the present study two types of power law are developed for the friction factor of commercial pipe, and explicit forms of equations are generated by applying the power law friction factor equations for the simple design of commercial pipes.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.4
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• pp.397-403
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• 1994

The seepage flow has been investigated conducting laboratory experiments mainly in order to determine the relation of seepage flow friction factor against Reynolds number. The apparatus of seepage flow measurements has the water flow almost horizontaly. Several sets of experiments were carried out, and various flow conditions were obtained in each set of flow. To cover wide range of flow conditions, used were various materials of different measurement sizes and various stages of water discharge in the seepage flow tests. Shape factor equation was developed using existing data, and based on the present laboratory data, an explicit equation was developed for the estimation of friction factor of seepage flow in the range of Reynolds number from about 1 to about 600. The same equation is expected for the flow condition of Reynolds number over 600, considering the trend of friction factor distribution.