Judul: Rancang Bangun Pompa Hydram di Sungai Ciapus dan Sungai Cihideung, Bogor, Jawa Barat
Abstrak: Sungai Cihideung dan Ciapus merupakan anak dari Sungai Cisadane yang melewati daerah kampus Institut Pertanian Bogor. Menanggulangi permasalahan penyediaan air khususnya untuk kegiatan pertanian, maka penggunaan pompa hydraulic ram (hydram) mempunyai prospek yang sangat baik. Pompa hydram memanfaatkan tenaga air yang jatuh dari tempat suatu sumber sebagai sumber energi untuk bekerja. Penelitian ini bertujuan untuk menghasilkan prototipe pompa hydram, menghitung besar debit yang dihasilkan pada pompa hydram, dan menganalisis head pemasukan dan pemompaan yang memungkinkan untuk diterapkan. Hasil perancangan pompa hydram pada kedua sungai memiliki dimensi yang sama. Pompa hydram yang dirancang bangun memiliki diameter badan pompa sebesar 2 inch, diameter pipa suplai 2 inch, diameter pipa outlet 1 inch, dan volume tabung udara sebesar 4 liter. Pipa suplai dan outlet pada Sungai Cihideung memiliki panjang berturut-turut 28 m dan 125,65 m, sedangkan pada Sungai Ciapus memiliki panjang berturut-turut 30 m dan 116 m. Pengujian juga dilakukan terhadap pengaruh panjang pipa suplai terhadap debit hasil pemompaan. Hydram yang memiliki pipa suplai yang panjang akan memberikan gaya tekan yang lebih tinggi dibandingkan dengan pipa suplai yang pendek., The Cihideung and Ciapus Rivers are tributaries of the Cisadane River which pass through IPB University Campus area. To overcome the problem of water supply, especially for agricultural activities, the use of a hydraulic ram pump (hydram) has a very good prospect. The hydram pump utilizes the flow of energy that falls from a source as an energy source to work. The research aimed to produce a hydraulic ram pump prototype, calculate the amount of discharge generated at the hydraulic ram pump, and analyze an intake and pumping head that allows it to be applied. The results of the hydraulic ram pump design in both rivers had the same dimensions. The hydraulic ram pump was designed with a pump body diameter of 2 inches, a supply pipe diameter of 2 inches, an outlet pipe diameter of 1 inch, and an air tube volume of 4 liters. The supply and outlet pipes on the Cihideung River had a length of 28 m and 125.65 m respectively, whileon the Ciapus River had a length of 30 m and 116 m respectively. Tests were also carried out on the effect of the supply pipe length on the pumping discharge. Hydram with a long supply pipe will provide a higher compressive force than the short supply pipe.
Keyword: design, hydraulic ram, outlet pipe, supply 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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