Manning Roughness Coefficient Study on Bed Materials Non-Cohesive with Parameters Using Entropy to Open Channel Flow Students of Civil Engineering Undip

Dalam rekayasa hidraulik, koefisien perlawanan aliran atau koefisien kekasaran Manning adalah parameter penting dalam peramalan aliran pada saluran, merancang struktur hidraulik, perhitungan distribusi kecepatan, angkutan sedimen (Bilgil & Altun, 2008). Peramalan aliran sungai merupakan langkah yang sangat penting dalam rangka meningkatkan kebijakan pengelolaan yang ditujukan kepada penggunaan sumber daya air serta untuk mitigasi, pencegahan dan pertahanan tindakan terhadap degradasi lingkungan (Greco et al., 2014) aliran dalam saluran terbuka terbatas pada aspek perbandingan lebar – kedalaman tiga dimensi, dan tegangan geser dinding yang tidak terdistribusi secara merata di keliling penampang basah. Hal ini dikarenakan adanya permukaan bebas dan arus sekunder Suatu model matematika, yang berasal dari informasi penerapan teori maksimalisasi entropi pada data terkumpul, digunakan untuk mengevaluasi medan aliran dan menghitung debit air. Background

the first to investigate the Manning roughness coefficient on entropy parameters in the case of low flow regimes to obtain bed calculation on the boundary shear stress in an open channel boundary rectangular shape. Then, assuming a variety of slope sidewalls Purpose of Paper Knowledge of the velocity distribution in the cross section of the river is fundamental in hydraulic modeling of the river, sediment and pollutant transport, channel design, river training work and hydraulic structures as well as in the manufacture of curves rating. Aim of Paper

Kajian Teori

lanjutan g percepatan grafitasi

Lanjutan Didasarkan pada hipotesis fenomena dip Greco dan Mirauda (2012) telah menunjukkan bahwa, untuk saluran pada berbagai bentuk penampang, kecepatan maksimum yang berada di bawah permukaan bebas sekitar 20 ÷ 25% dari kedalaman maksimum

Lanjutan Hubungan antara letak Kecepatan Maksimum dan y maksimum serta Kedalaman (Mirauda & Grico, 2012)

lanjutan

Dengan demikian, y max sama dengan ¾ dari kedalaman air (h), dan α sama dengan 1/3

Lanjutan

Theoretical background According Chiu (1978,1987, 1988, 2002) or Choo (2002). the entropy function of velocity can be expressed as follows u is the time mean velocity distributed spatially over the cross-section of channel Umax indicates the maximum velocity f (u) is the probability density function of velocity The available information that imposes constraints on f(u)

Method of Lagrange maximizing H to the limiting factors λ1 and λ2 are lagrange multipliers

Parameter M and Probability Density Function f(u/umax)

Bed roughness and water surface acts on the flowing water Flow zones

I- laminar flow II- log-law velocity distribution III- wake region IV- free surface region

Flow zones flat bed II I III IV

Flow zones rough bed I II III IV

Flow zones [Williams J.J., 1996]

Bed roughness and water surface acts on the shape of flowing water velocity profile. Flow zones

The shape of velocity profile depend on: flow depth, av. velocity of flowing water, bed roughness, relative roughness... For hydraulically rough flow conditions I and IV flow zone decreases Fr = 0.074Fr = D Flow zones

Laboratory measurements Flume dimensions: l2.0 x 0.5 x 0.6 m (glass walls) Flume rig: micro-propeller flow-meter slope measurements Bed slope, water surface slope Discharge: max 0.13 qm s -1 Artificial grains Ø – 4 to 8 cm

Bed roughness measurements homogeneous roughness k s = K (1.926 SF 2 – SF ) Profile-meter AG-1

Log-law velocity distribution Maximum velocity moves with relative roughness change flat bed

Log-law velocity distribution Maximum velocity moves with relative roughness change rough bed

Log-law velocity distribution For the same bed roughness curves are parallel flat bed

Log-law velocity distribution For the same bed roughness curves are parallel grains 4M

Log-law velocity distribution For the same bed roughness curves are parallel grains 4D

Log-law velocity distribution For the same bed roughness curves are parallel grains 6D

Log-law velocity distribution For the same bed roughness curves are parallel grains 8D

Calculation of velocity and shear stresses Log-law velocity distribution for whole profile is used U/U max = A log (y/Y) + B Modified Prandtl equation B becomes constant -B = 1.12 ± 3%

Calculation of velocity and shear stresses U/U max = A log (y/Y) + B A value changes with relative depth Y/K

Calculation of velocity and shear stresses U/U max = A log (y/Y) + B Comparison of measured to calculated A constant

Calculation of velocity and shear stresses Velocity profile reflects shear stresses Use of logarithmic equation allow calculating  0 for rough flow conditions  0 = K U M

Calculation of velocity and shear stresses

Conclusions Near bed the velocity and velocity profile slope calculations (in logarithmic scale) are correct within the second and third flow zone. The use of equation (4) makes the bed level (zero velocity) estimation error negligible (B=1.12). The use of mentioned method is limited to the rough flow conditions where the maximum velocity lays close to the water surface (the near surface region decreases to 20% of water depth). The measurements of surface velocity, water depth and bed roughness can be used for calculation of water velocity profile and bed shear stresses for rough flow conditions.