Phân tích độ nhậy của phương pháp xác định hệ số nhám sử dụng tài liệu đo lưu tốc

Việc xác định hệ số nhám Manning n có một ý nghĩa quan trọng trong tính toán thủy lực nói chung và thủy lực dòng hở nói riêng. Một trong những phương pháp đo đạc dòng chảy trong sông khá phổ biến là đo lưu tốc tại hai điểm ở 0.8 và 0.2 lần của độ sâu dòng chảy. Những số liệu này có thể áp dụng để xác định hệ số nhám dựa trên qui luật phân bố logarit của vận tốc trong dòng chảy rối. Bài báo này khảo sát lại phương pháp xác định hệ số nhám sử dụng số liệu đo lưu tốc và phân tích độ nhạy của kết quả tính toán bằng lý thuyết và thực nghiệm.
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Phân tích độ nhậy của phương pháp xác định hệ số nhám sử dụng tài liệu đo lưu tốc BÀI BÁO KHOA HỌC SENSITIVE ANALYSIS OF ROUGHNESS COEFFICIENT ESTIMATION USING VELOCITY DATA Nguyen Thu Hien1 Abstract: An accurate estimation of Manning’s roughness coefficient n is of vital importance in any hydraulic study including open channel flows. In many rivers, the velocities at two-tenths and eight-tenths of the depth at stations across the stream are available to estimate Manning’s roughness n based on a logarithmic velocity distribution. This paper re-investigates the method of the two-point velocity method and a sensitive analysis is theoretically carried out and verified with experiment data. The results show that velocity data can be used to estimate n for fully rough- turbulent wide channels. The results also indicate that the errors in the estimated n are very sensitive to the errors in x (the ratio of velocity at two-tenths the depth to that at eight-tenths the depth). The theoretical and experimental work shows that the smoother and deeper a stream, the more sensitive the relative error in estimated n is to the relative error in x. Keywords: open channels, roughness coefficient, two-point velocities, logarithm distribution. 1. INTRODUCTION* narrow range of river conditions and the An accurate estimation of Manning’s accuracy is still questionable. roughness coefficient n is of vital importance In many rivers, a common method to in any hydraulic study including open measure stream flow is to measure velocity in channel flows. This also has an economic several verticals at 0.2 and 0.8 times the depth significance. If estimated roughness with the velocity distribution depends on the coefficient are too low, this could result in roughness height. This may be related to over-estimated discharge, under-estimated Manning’s n. For wide channels with flood levels and over-design and unnecessary reference to the logarithmic law of velocity expense of erosion control works and vice distribution then the value of n can be versa (Ladson et al., 2002). determined based on this velocity data (Chow, The direct method to determine the value of 1959 and French, 1985). In practice, velocity roughness (Barnes, 1967, Hicks and Mason, measurement errors were unavoidable. In this 1991) is time consuming and expensive because paper, the two-point velocity method is re- friction slopes, discharges and some cross investigate and a sensitive analysis is sections must be measured. Current practice theoretically carried out and verified with many indirect or indirectly methods have been experiment data. used to estimate roughness in streams from 2. THEORY experience or some empirical relationship based 2.1 Relationship between velocity on the particle size distribution curve of surface distrubution and roughness bed material (Chow, 1959, French 1985, The velocity distribution of uniform turbulent Barnes, 1967, Hicks and Mason, 1991, Coon, flow in streams can be derived by using 1998, Dingman and Sharma, 1997). However Prandtl’s mixing length theory (Schlichting, these methods are often applicable only to a 1960). Based on this theory, the shear stress at any point in a turbulent flow moving over a 1 Hydraulic Department, Thuyloi University solid surface can be expressed as: KHOA HỌC KỸ THUẬT THỦY LỢI VÀ MÔI TRƯỜNG - SỐ 64 (3/2019) 113  2  du  where, in this case, m is a coefficient   l 2   (1) approximately equal to 1/30 for sand grain  dz  where  is the mass density of the fluid, l is roughness (Keulegan 1938). Substituting Equation (6) for z0 in Equation (5) yields the characteristic length known as the mixing u 30 z length ( l  z ,where  is known as von u  * ln (7)  ks Kármán’s turbulent constant. The value of  determined from many experiments is 0.4), u is for mean velocity of turbulent flow for fully- velocity at a point, and z is the distance of a rough flow in a wide channel (Keulegan,1938): point from the solid surface. V R  6.25  2.5 ln (8) The shear stress  is equal to the shear stress U* ks on the bed  0 of the flow in the channel. From where V and U * are cross-sectional mean these two assumptions, Equation (1) can be velocity and shear velocity respectively and R is written as hydraulic radius. 1  0 dz In natural wide streams, the flow is usually du  (2) fully rough-turbulent, and the logarithmic law of   z velocity distribution depending on the Integrating Equation (2) gives roughness height (Equations (7) and (8)) can b ...