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"Turunan formula Navier-Stokes dipakai untuk menghitung kerugian tekanan aliran dalam pipa. Panjang pipa, diameter pipa, kecepatan fluida, kekasaran permukaan dan koefisien gesek yang mempengaruhi nilai kerugian tekanan. Formula tersebut tidak berlaku pada belokan/cabang pipa, setelah katup, adanya perubahan diameter (unsteady flow), adanya getaran, dll. Drag reduction dari solusi surfactant atau biopolymer telah menarik perhatian dari sisi konversi energy, dikarenakan penurunan secara mekanis tidak terjadi tetapi menghasilkan drag reduction yang besar di kondisi konsentrasi tertentu oleh karena itu solusi biopolymer banyak digunakan pada system pemipaan dan hasil percobaan dilapangan menunjukan penurunan dari tenaga yang dibutuhkan pompa mencapai 30% dari kecepatan aliran normal Penelitian ini bertujuan untuk membuktikan efek panjang aliran terhadap aliran berkembang penuh dengan membandingkan 3 macam fluida yaitu air murni ; biopolimer air tape ketan 100 ppm dan biopolimer air tape ketan 250 ppm. Di mana biopolimer merupakan hasil fermentasi beras. dan membuktikan keterbatasan penggunaan formula Navier-Stokes. Eksperimen ini menggunakan pipa acrylic berdiameter 12 mm. Variasi panjang pipa masuk terhadap titik pengukur tekanan (pressure tap) yaitu dengan menggeser pipa kecil masuk kedalam pipa uji hingga keadaan fluida mencapai kondisi berkembang penuh. Pada pipa uji dipasang 4 buah pressure tap dengan jarak masing-masing tap 250 mm. Air murni sebagai fluida uji. Debit yang keluar diukur dengan gelas ukur pada periode waktu untuk mendapatkan nilai bilangan Reynolds. Hasil menunjukkan bahwa karakteristik panjang aliran berkembang penuh untuk fluida dengan campuran konsentrasi biopolymer lebih besar dibandingkan dengan air murni.

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Navier-Stokes equations derived formula used to calculate the pressure loss in pipe flow. The length of the pipe, the pipe diameter, the fluid velocity, surface roughness and coefficient of friction that affect the value of pressure loss. The formula does not apply to the branch / branch pipes, the valves, the change in diameter (unsteady flow), the presence of vibration, etc.. Drag reduction of surfactant solution or a biopolymer has attracted attention from the conversion of energy, due to a mechanical reduction does not occur but produced a large drag reduction in a specific concentration of condition therefore biopolymer solutions are widely used in piping systems and field experimental results show a decrease of available power pumps needed to reach 30% of normal flow velocity.

This study aims to prove the effect of flow length to the flow is fully developed by comparing three kinds of fluid that is pure water, 100 ppm biopolymer and 250 ppm biopolymer. Where biopolymer is fermented rice and prove the limitations of the use of the Navier-Stokes formula. These experiments using 12 mm diameter acrylic pipe. Length variation on the point of intake pressure gauge (pressure tap) that is by sliding a small pipe into the test tube until the fluid reaches the state is fully developed conditions. In test tube fitted with a pressure tap four fruit each tap distance 250 mm. Pure water as test fluid. The exit discharge is measured with a measuring cup in the period of time to get the value of Reynolds number. Results showed that the characteristic length for the fluid flow is fully developed with a mixture of biopolymer concentration greater than pure water. "

"Persamaan Euler merupakan salah satu penyederhanaan persamaan Navier-Stokes dengan asumsi inviscid, adiabatik serta menghilangkan efek dari body force. Pada aliran kompresibel, persamaan Euler merupakan sistem pesamaan hiperbolik non-linear untuk hukum konservasi. Pada aliran kompresibel, munculnya fenomena diskontinuitas berupa gelombang kejut sering menimbulkan masalah dalam simulasi, terutama dalam hal akurasi. Pada skema Godunov, akurasi interpolasi untuk memperoleh fluks pada batas antar sel dapat ditingkatkan dengan penggunaan limiter. Salah satu limiter orde tinggi yang dapat digunakan dalam penyelesaian persamaan Euler adalah skema weighted essentially non-oscillatory (WENO). Masalah yang timbul dari penggunaan skema WENO sebagai limiter adalah beban komputasi yang sangat tinggi, terlebih jika sistem persamaan dan domain komputasi yang kompleks. Pengurangan beban komputasi dapat dilakukan dengan cara simplifikasi skema WENO itu sendiri atau dengan menggunakan skema hibrid dimana skema WENO akan digunakan pada kondisi tertentu. Pada penelitian ini dikembangkan skema hibrid orde tinggi yang mengadopsi WENO pada daerah diskontinu dengan deteksi diskontinuitas secara lokal. Metode cell-centered finite volume digunakan untuk diskretisasi ruang. Penyelesaian masalah Riemann pada batas sel digunakan skema Harten-Lax-van Leer contact (HLLC) dan Lax-Friedrichs, serta untuk integrasi waktu digunakan skema strong stability preserving Runge-Kutta orde ketiga untuk memberikan kestabilan yang baik pada skema numerik. Berdasarkan hasil yang diperoleh, skema hibrid yang dikembangkan cukup efektif digunakan dalam penyelesaian masalah aliran kompresibel. Pengurangan waktu komputasi yang signifikan dan akurasi yang baik menjadikan skema hibrid yang dikembangkan menjadi salah satu pilihan skema numerik orde tinggi yang baik untuk dapat diterapkan dalam simulasi aliran kompresibel.

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Euler equation is a simplification of Navier-Stokes equation which assume the flows are inviscid, adiabatic, and eliminating the effects of body forces. In the compressible flow, the Euler equation is a non-linear hyperbolic conservation laws. The presence of the discontinuities phenomenon in the form of shock wave in the compressible flow often arise the problem in the simulation, mainly in the terms of accuracy. In the Godunovs scheme, the accuracy of interpolation to obtain flux at the intercell boundary can be improved by using a high order limiter. One of the high order limiter that can be used to solve the Euler equation is weighted essentially non-oscillatory (WENO) scheme.

The problem that arises from the use of WENO scheme is high computational loads, moreover the system of equations or the domain are very complex. To reduce the computational cost, it can be done by simplify the WENO reconstruction or implement the hybrid scheme where the WENO scheme only applied in certain conditions.

In this study, hybrid high order scheme are developed which adopt the WENO schem in the discontinuous region by detecting the local discontinuities. The cell-centered finite volume are used in the spatial discretization. Harten-Lax-van Leer contact (HLLC) and Lax-Friedrichs scheme are used to solve Riemann problem in the cell boundary, and third order strong stability preserving Runge-Kutta (SSP-RK) scheme is used for time integration to ensure the positivity and provide good stability in the numerical scheme.

The results shows that the hybrid scheme developed in this work are effective for solving compressible flow problem. The significant reduction of the computational cost and the satisfactory accuracy results are make this hibrid scheme become one of the good choices of high order numerical scheme to be applied in the compressible flow simulation."

"Pengurangan hambatan serat dalam larutan air telah dipelajari sebagai fungsi konsentrasi dengan menggunakan pipa spiral. Percobaan dilakukan dengan mengukur pressure drop .Tujuan penelitian ini untuk meneliti pressure drop dalam pipa spiral dengan penambahan serat dalam larutan air. Pipa Spiral dengan diameter yang berbeda yaitu 25 mm dan 27 mm digunakan dalam penelitian ini dengan variasi serat daun nanas konsentrasi 500 ppm dan 1000 ppm. Ditemukan bahwa serat daun nanas mengalami pengurangan hambatan pada aliran turbulen. Percobaan dilakukan dari bilangan Reynolds rendah sampai tertinggi yaitu 29500. Penulis mengamati rasio penurunan hambatan maksimum yaitu 16.5 % pada bilangan Reynolds 29500 dengan konsentrasi larutan serat 1000 ppm. Penurunan koefisien gesek mengindikasikan keefektifan fluida uji sebagai drag reduction agent.

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The drag reduction of dispersions of fibers in aqueous solutions of was studied as a function of concentration with circular pipes apparatus. The experiments were carried out by measuring the pressure drop. The purpose of this research is to investigate the reduction of pressure drop in a circular pipe with the addition of fiber in aqueous solution. Circular pipe with diameter of 25 mm and 27 mm are used in this study. Concentration of pineapple leaf fiber solutions are 500 ppm and 1000 ppm.

It was found that fiber solutions give rise to drag reduction in turbulent flow range. The experimental was conducted from low to high Reynolds number about 29500. We observed a maximum drag reduction ratio of 16.5 % at Reynolds number 29500 with fiber solutions concentration of 1000 ppm. The pressure drop measurements indicate the effectiveness of pineapple leaf fiber as drag reduction agent."

"Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The book explains the principles of these subjects. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the Navier-Stokes equations. When the book was written, the main intent was to write a text on initial-boundary value problems that was accessible to a rather wide audience. Therefore, functional analytical prerequisites were kept to a minimum or were developed in the book. Boundary conditions are analyzed without first proving trace theorems, and similar simplications have been used throughout. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis."

"This second edition, like the first, attempts to arrive as simply as possible at some central problems in the Navier-Stokes equations in the following areas: existence, uniqueness, and regularity of solutions in space dimensions two and three; large time behavior of solutions and attractors; and numerical analysis of the Navier-Stokes equations. Since publication of the first edition of these lectures in 1983, there has been extensive research in the area of inertial manifolds for Navier-Stokes equations. These developments are addressed in a new section devoted entirely to inertial manifolds. Inertial manifolds were first introduced under this name in 1985 and, since then, have been systematically studied for partial differential equations of the Navier-Stokes type. Inertial manifolds are a global version of central manifolds. When they exist they encompass the complete dynamics of a system, reducing the dynamics of an infinite system to that of a smooth, finite-dimensional one called the inertial system. Although the theory of inertial manifolds for Navier-Stokes equations is not complete at this time, there is already a very interesting and significant set of results which deserves to be known, in the hope that it will stimulate further research in this area. These results are reported in this edition. Part I presents the Navier-Stokes equations of viscous incompressible fluids and the main boundary-value problems usually associated with these equations. The case of the flow in a bounded domain with periodic or zero boundary conditions is studied and the functional setting of the equation as well as various results on existence, uniqueness, and regularity of time-dependent solutions are given. Part II studies the behavior of solutions of the Navier-Stokes equation when t approaches infinity and attempts to explain turbulence. Part III treats questions related to numerical approximation. In the Appendix, which is new to the second edition, concepts of inertial manifolds are described, definitions and some typical results are recalled, and the existence of inertial systems for two-dimensional Navier-Stokes equations is shown."

"Untuk meningkatkan performa dan efisiensi mikro gas turbin proto X1, telah dilakukan analisa tentang adanya presure drop pada elbow saluran masuk ruang bakar. Penelitian ini dilakukan untuk mengamati fenomena aliran fluida dan distribusi tekanan yang terjadi pada elbow 900 menggunakan SolidWorks 2011. Penelitian dilakukan dengan membandingkan besarnya pressure drop akibat penambahan guide vanes pada elbow 90°. Hasil penelitian menunjukkan pressure drop berkurang dengan adanya penambahan guide vanes pada elbow bagian bawah sebesar 0,54 % pada kecepatan aliran 5,73 m/s, 10,42% pada kecepatan aliran 6,78 m/s, dan sebesar 11,29% pada kecepatan aliran 7,72 m/s. Dari hasil penelitian penulis menyarankan agar dilakukan analisa terhadap pressure drop yang terjadi pada ruang bakar sehingga performa dan efisiensi turbin dapat ditingkatkan lagi.

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To improve performance and efficiency of micro gas turbine proto X1, has conducted an analysis of the presure drop in the combustion chamber inlet elbow. This study was conducted to observe the phenomenon of fluid flow and pressure distribution that occurs at elbow 900 using SolidWorks 2011. The study was conducted by comparing the magnitude of pressure drop due to the addition of guide vanes in the elbow 90°.

The results show pressure drop decreases with the addition of guide vanes in the elbow at the bottom of 0.54% at a flow rate of 5.73 m /s, 10.42% at a flow rate of 6.78 m/ s,and by 11.29% at a flow rate of 7.72 m /s. From the results of the study research suggested that the analysis performed on the pressure drop that occurs in the combustion chamber so that the performance and efficiency of the turbine can be increased again."

"Turunan formula Navier-Stokes dipakai untuk menghitung kerugian tekanan aliran dalam pipa. Panjang pipa, diameter pipa, kecepaan fluida, kekasaran permukaan dan koefisien gesek yang mempengaruhi nilai kerugian tekanan. Formula tersebut tidak berlaku pada belokan/cabang pipa, setelah katup, adanya perubahan diameter (unsteady flow), adanya getaran, dll. Tujuan penelitian adalah melihat pengaruh panjang aliran hidrodinamik pada pipa masuk (inlet) terhadap nilai kerugian tekanan aliran dalam pipa dan membuktikan keterbatasan penggunaan formula Navier-Stokes. Eksperimen ini menggunakan pipa acrylic berdiameter 12 mm. Variasi panjang pipa masuk terhadap titik pengukur tekanan (pressure tap) yaitu dengan menggeser pipa kecil masuk kedalam pipa uji hingga keadaan fluida mencapai kondisi berkembang penuh. Pada pipa uji dipasang 4 buah pressure tap dengan jarak masing-masing tap 250 mm. Air murni sebagai fluida uji. Debit yang keluar diukur dengan gelas ukur pada periode waktu untuk mendapatkan nilai bilangan Reynolds. Hasil menunjukkan bahwa karakteristik panjang aliran berkembang penuh untuk aliran laminer adalah rasio L/D = ± 0,05*Re dan pada aliran turbulen yaitu L/D = ± 4,4*Re1/6.

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Differential Navier-stokes formula is used to calculate a pressure loss in a pipe. Pressure loss in pipe influenced by the pipe length, the pipe diameter, the fluid velocity, surface roughness of pipe and friction coefficient. This formula could not be applied to the turning or branch of the pipe, after the valve, pipe in which its diameter has changed (unsteady flow), shock or vibration occurs, etc. The goal of this study is to measure the influence of inlet pipe length to the value of pressure loss in pipe and to proved the limitation in order to use the Navier-Stokes formula. This experiment used acrylic pipe with 12 mm diameter. Variation of inlet pipe length to first pressure tap are 50D, 70D, 100D and 130D. Variation the length of inlet pipe is arranged by put the inlet pipe into the test pipe. On the test pipe are used four pressure taps with 25 cm distance. Displacement the inlet pipe into first pressure tap will be effected to the value of pressure in the manometer.Water as a test fluid. Debit or rate of the flow is measured in period of time to get Reynolds number. The results had showed that the characteristic of fully developed flow lenght for the laminar flow is shown by L/D ratio = 0.05*Re and in turbulent flow L/D ratio = 4.4*Re1/6"