Judul: Design Of Irrigation Water Supply For  Dramaga Seedbed Using Hydram Pump Sourcing from Ciapus River
Abstrak: Kekeringan merupakan kejadian alam yang disebabkan oleh rendahnya curah hujan dalam periode waktu tertentu sehingga menyebabkan kurangnya ketersediaan atau suplai air untuk kegiatan manusia dan lingkungan. Jumlah ketersediaan air menurun sehingga berbagai sektor mengalami kekurangan air, salah satunya ialah sektor pertanian. Sektor pertanian yang kekurangan air dapat menurunkan produktivitas dalam proses pemanenannya. Salah satu cara untuk menanggulanginya ialah dengan memanfaatkan pompa hidraulik ram. Debit penggerak pompa hidram yang diperoleh sebesar 16.4 liter/detik. Berdasarkan hasil pengukuran beda elevasi, beda elevasi sumber terhadap pompa (supply head) sebesar 1 meter diperoleh dengan jarak sepanjang 30 meter. Diketahui bahwa beda elevasi antara titik pemompaan dan daerah layanan sebesar 12.87 meter. Pompa hidram yang digunakan merupakan pompa hidram Sanan tipe Flap dengan ukuran pipa input 4 inchi dan output 2 inchi. Rasio tinggi jatuh dan tinggi angkat digunakan 1 : 13.5 sehingga estimasi debit pemompaan mencapai 0.354 liter/detik. Sistem jaringan pipa transmisi akan mengalami kerugian head akibat jenis pipa yang digunakan dan belokan pada pipa. Hasil penelitian menunjukkan bahwa total kerugian head akibat gesekan dan belokan pada pipa adalah 0.58 meter. Total head pemompaan ialah sebesar 13.6 meter., Drought is a natural event caused by low rainfall in a certain period of time, causing a lack of availability or supply of water for human activities and the environment. The agricultural sector that lacks water can reduce productivity in the harvesting process. One way to overcome this is to use a ram hydraulic pump. The hydraulic ram pump drive discharge obtained is 16.4 liters/second. Based on the measurement results of elevation difference, the difference in elevation of the source to the pump (supply head) of 1 meter is obtained with a distance of 30 meters. It is known that the elevation difference between the pumping point and the service area is 12.87 meters. The hydraulic ram pump used is a Flap type Sanan hydram pump with a 5 inch input pipe size and 3 inch output. The ratio of falling height and lifting height is used 1 : 13.5 so that the estimated pumping discharge reaches 0.354 liter/second. The transmission pipeline sistem will experience head losses due to the type of pipe used and the bend in the pipe. The results showed that the total head loss due to friction and bends in the pipe was 0.58 meters. The total pumping head is 13.6 meters.
Keyword: Ciapus river, hydram pump, supply pipe, transmission pipe

Judul: Application of the Hydram Pump on Cihideung River as a Water Supply System for Leuwikopo Experimental Field Bogor Regency
Abstrak: Pemenuhan kebutuhan air untuk kebun percobaan sangat diperlukan sebagai upaya peningkatan hasil yang diharapkan. Selama ini kebutuhan air di lahan Leuwikopo hanya dipenuhi dari air hujan dan air tanah, sedangkan Sungai Cihideung yang dekat belum dimanfaatkan dengan baik. Penelitian ini bertujuan untuk mengetahui debit suplai, menghasilkan rancangan pipa transmisi, dan desain instalasi penerapan pompa hidram. Penelitian dimulai dengan mengukur beda elevasi dari rencana titik pengambilan, titik pompa hidram, dan titik reservoir. Selanjutnya dilakukan perhitungan debit suplai dengan metode Iversen, penentuan dimensi pipa suplai berdasarkan metode Calvert, perancangan perpipaan dengan perhitungan head loss, dan penentuan spesifikasi pompa hidram di pasaran. Hasil penelitian menunjukkan debit penggerak pompa hidram sebesar 8,22 l/detik. Jaringan perpipaan pada pipa suplai sepanjang 28 m dengan diameter 4 in berbahan PVC dan pipa penghantar sepanjang 140 m dengan diameter 2 in berbahan HDPE. Rancangan desain instalasi pada intake menggunakan drum berkapasitas 120 l yang diberi lubang. Pompa hidram yang digunakan adalah pompa merek Sanan tipe Flap 4 dengan estimasi debit pemompaan sebesar 0,341 l/detik atau 29.462 liter/hari., Meeting the water needs for experimental field is very necessary as an effort to increase the expected yields. So far, the fulfillment of water needs in the Leuwikopo field is only from rainwater and ground water, while the Cihideung River which is close has not been used properly. This study aimed to determine the supply flowrate, produce a transmission pipe design, and design the installation of a hydraulic ram pump. The study begined by measuring the elevation difference from the planned intake point, hydram pump point, and reservoir point. Furthermore, calculating the supply discharge using the Iversen method, determining the supply pipe based on the Calvert method, designing a piping network with head loss calculations, and determining the hydram pump specification in the market. The results showed that the flowrate of the hydraulic ram pump was 8,22 l/second. The piping network in the supply pipes was 28 m long with a diameter of 4 in and was made of PVC, while the delivery pipes with 140 m long and 2 in diameter was made of HDPE. The installation design at the intake was designed using a drum with capacity of 120 l and had a hole. The hydraulic ram pump used was a Sanan pump type Flap 4 with an estimated pumping discharge of 0,341 l/second or 29.462 l/day.
Keyword: debit suplai, desain, pompa hidram

Judul: Penentuan Nilai Eigen dan Vektor Eigen dari Matriks Tridiagonal 2-Toeplitz dengan Pendekatan Polinomial Chebyshev
Abstrak: The eigenvalues and eigenvectors of a matrix can be determined by finding its characteristic polynomials. The characteristic polynomials of a tridiagonal 2-Toeplitz matrix is shown to be closely connected to polynomials which satisfy the Chebyshev recurrence relationship. If the order of the matrix is odd, then the eigenvalues are found explicitly in terms of the Chebyshev zeros and the eigenvectors are found in terms of the polynomials satisfying the recurrence relationship. For even ordered matrices, the situation is more complicated. The problem in these cases is that although the Chebyshev recurrence formula is still applied, its initial values are not generating Chebyshev polynomials
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