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: Potensi Aliran Sungai Cihideung Sebagai Sumber Air Irigasi Kebun Percobaan Leuwikopo Menggunakan Pompa Hidram
Abstrak: Sungai Cihideung merupakan anak Sungai Cisadane yang dimanfaatkan untuk berbagai kegiatan oleh masyarakat di sekitar Kampus IPB Dramaga. Daerah Leuwikopo yang berada dekat dengan Sungai Cihideung memperoleh air dari hujan dan air tanah. Pemanfaatan air tanah ini memerlukan pompa listrik dan membutuhkan biaya pengoperasian. Pompa hidram dapat menjadi solusi untuk menekan biaya penyaluran air. Untuk itu diperlukan debit sumber air yang sesuai sebagai sumber energi penggerak pompa. Penelitian ini dilakukan untuk menentukan lokasi instalasi pompa hidram, mengetahui profil muka air dan kecepatan aliran, serta menentukan potensi aliran air Sungai Cihideung. Perhitungan debit berdasarkan SNI 8066:2015 dan metode cubic spline interpolation. Lokasi yang dipilih untuk pemasangan pompa berada pada 6o33'57.7" LS dan 106o43'33.09" BT di tepi Sungai Cihideung. Sungai Cihideung memiliki lebar 20,2 m dengan ketinggian air 0,83 hingga 0,86 m dengan kecepatan aliran yang terukur antara 0 hingga 0,3 m/detik. Debit maksimum Sungai Cihideung sebesar 2,47 m3/detik sedangkan debit minimum sebesar 2,17 m3/detik dengan debit rata-rata 2,30 m3/detik. Dari kurva liku kalibrasi debit didapatkan persamaan Q = 167.63H25.697 dengan koefisein determinasi sebesar 0,92., Cihideung River is a tributary of the Cisadane River and was used for various activities by the communities around the IPB Dramaga Campus. The Leuwikopo area was close to the Cihideung River, and got water from rain and groundwater. Utilization of groundwater needed electric pump and required operational costs. Hydram ram pump can become a solution to reduce operational cost. Several condition of water source discharge were needed as the driving energy to operate these pump. This research was conducted to determine the location of hydraulic ram pump installation, to know the water level profile and flow velocity, and to determine the potential discharge of Cihideung River. The discharge was calculated based on SNI 8066:2015 and the cubic spline interpolation method. The selected location of hydraulic ram pump was at 6o33'57.7" S and 106o43'33.09" E on the banks of the Cihideung River. Cihideung River has a width of 20.2 m with a water level around 0.83 to 0.86 meters and the flow velocity was measured around 0 to 0.3 m/s. The maximum discharge of the Cihideung River was 2.47 m3/s while the minimum was 2.17 m3/s with mean discharge of 2.30 m3/s. The equation of rating curve was Q = 167.63H25.697 with a determination coefficient of 0.92.
Keyword: potensi debit, Sungai Cihideung, tinggi muka air

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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