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1

Steady Oseen’s flow past a deformed sphere: an analytical approach

Srivastava D. K., Yadav R. R., Yadav S.

Journal of Theoretical and Applied Mechanics

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2013

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Vol. 51 nr 3

661--673

EN

In a recent authors’ paper, the general expression of Stokes drag experienced by a deformed sphere in both longitudinal and transverse flow situations was calculated in terms of the deformation parameter up to the second order. In this paper, Oseen’s correction to the axial Stokes drag on the deformed sphere is presented by using Brenner’s formula in general, first and then applied to prolate and oblate the deformed spheroid up to the second order of the deformation parameter. Numerical values of Oseen’s correction is obtained with respect to the deformation parameter and Reynolds number. The corresponding variations are depicted in figures. Some particular cases of a needle shaped body and flat circular disk are considered and found to be in good agreement with those existing in the literature. The import ant applications are also highlighted.

2

Generalized perfect numbers

Shukla D. P., Yadav S.

Commentationes Mathematicae

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2013

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Vol 53, No. 1

61--72

EN

In this paper a modified form of perfect numbers called (p, q)+ perfect numbers and their properties with examples have been discussed. Further properties of σ+ arithmetical function have been discussed and on its basis a modified form of perfect number called (p, q)+ super perfect numbers have been discussed. A modified form of perfect number called (p, 0)-perfect and their characterization has been studied. In the end of this paper almost super perfect numbers have been introduced.

3

Stokes flow around slowly rotating concentric previous spheres

Srivastava D. K., Yadav R. R., Yadav S.

Archive of Mechanical Engineering

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2013

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Vol. LX, nr 2

165--184

EN

In this paper, the problem of concentric pervious spheres carrying a fluid sink at their centre and rotating slowly with different uniform angular velocities Ω1, Ω2 about a diameter has been studied. The analysis reveals that only azimuthal component of velocity exists and the torque, rate of dissipated energy is found analytically in the present situation. The expression of torque on inner sphere rotating slowly with uniform angular velocity Ω1, while outer sphere also rotates slowly with uniform angular velocity Ω2, is evaluated. The special cases like, (i) inner sphere is fixed (i.e. Ω1 = 0), while outer sphere rotates with uniform angular velocity Ω2, (ii) outer sphere is fixed (i.e. Ω2 = 0), while inner sphere rotates with uniform angular velocity Ω1, (iii.) inner sphere rotates with uniform angular velocity Ω1, while outer rotates at infinity with angular velocity Ω2; have been deduced. The corresponding variation of torque with respect to sink parameter has been shown via figures. AMS subject classification – 76 D07.

PL

W artykule rozważa się problem koncentrycznych kul przepuszczalnych, ze zlewem płynu w centrum, które wirują powoli wokół średnicy z jednostajnymi prędkościami kątowymi Ω1 i Ω2. Analiza wykazała, że istnieje tylko azymutalny składnik prędkości, a moment obrotowy i szybkość rozpraszania energii są w istniejących warunkach wyznaczane analitycznie. Wyprowadzono wyrażenie na moment obrotowy na powierzchni wewnętrznej kuli powolnie wirującej z jednostajną prędkością kątową Ω1, podczas gdy kula zewnętrzna także powolnie wiruje z jednostajną prędkością kątową Ω2. Zbadano także przypadki szczególne, takie jak: (i) kula wewnętrzna jest nieruchoma (tzn. Ω1 = 0), podczas gdy kula zewnętrzna wiruje z jednostajną prędkością kątową Ω2, (ii) kula zewnętrzna jest nieruchoma (tzn. Ω2 = 0), podczas gdy kula wewnętrzna wiruje z jednostajną prędkością kątową Ω1, (iii) kula wewnętrzna wiruje z jednostajną prędkością kątową Ω1, podczas gdy kula zewnętrzna wiruje w nieskończonej odległości z prędkością kątową Ω2. Na wykresach przedstawiono zależności między zmianami momentu obrotowego a parametrami zlewu.

4

Composition of arithmetical functions with generalization of perfect and related numbers

Shukla D. P., Yadav S.

Commentationes Mathematicae

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2012

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Vol. 52, [Z] 2

153--170

EN

In this paper we have studied the deficient and abundent numbers connected with the composition of φ,φ*, σ,σ* and ψ arithmetical functions , where φ is the Euler totient, φ* is the unitary totient, σ is the sum of divisors, σ* is the unitary sum of divisors and ip is the Dedekind function. In 1988, J. Sandor conjectured that ψ(φ(m))≥m, for all odd m and proved that this conjecture is equivalent to ψ(φ(m))≥m/2 for all m. Here we have studied this equivalent conjecture. Further, a necessary and sufficient conditions of primitivity for unitary r-deficient numbers and unitary totient r-deficient numbers have been obtained . Finally, we have discussed the generalization of perfect numbers for an arithmetical function Eα.

5

Characterization of dead weight testers and computation of associated uncertainties: a case study of contemporary techniques

Yadav S.

Metrology and Measurement Systems

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2007

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Vol. 14, nr 3

453-469

EN

Estimation of uncertainty associated with pressure, measured by a dead weight tester is a key issue of recent times in pressure metrology. Though two different techniques have been used in the past yet there has been little uniformity in the way in which the measurement uncertainties of dead weight piston testers are evaluated and expressed. One of the techniques described in EAL document follows the universal approach based on ISO Guide and the relatively recent approach described in the National Accreditation Board of Laboratories (NABL-141) document presents a method for evaluating uncertainty in pressure measurement using dead weight testers through statistical analysis and error evaluated through linear curve fitting. This method is though in line with ISO Guide on the expression of uncertainty in measurement but differs from the traditional uncertainty measurement computations. The present paper describes a comparative study of these two different approaches through a case study carried out on an industrial dual range simple type dead weight tester. The paper also highlights some of the facts: how the new estimates affect pressure measurement and their commercial implementation and the benefits over traditional estimates.

6

Proficiency testing (PT) program under NABL in the pressure range 7-70 MPa using digital pressure calibrator (DPC)

Yadav S., Bandyopadhyay A. K.

Metrology and Measurement Systems

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2005

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Vol. 12, nr 3

323-340

EN

This paper describes the proficiency testing of the seven laboratories, accredited by National Accreditation Board for Testing and Calibration of Laboratories (NABL), India using a Digital Pressure Calibrator (DPC) [Model No. - H540/101, SI. No. - MC808, make-DH-Budenberg, U.K.] as an artifact in the pressure range 70 bar to 700 bar (7 MPa to 70 MPa). The primary objective for organizing this proficiency testing (PT) is to assess the laboratory's technical competence to perform measurements and also fulfilling the requirement of ILAC/APLAC in regards to the compatibility of results submitted by these laboratories. National Physical Laboratory (NPLI), New Delhi, India has the responsibility of coordinating this programme and also acted as a reference laboratory. The stability of the artifact was assessed by measurements made at NPLI before and after the circulation of the artifact. The comparison was carried out at 11 arbitrarily chosen pressure points i.e. 0.7 MPa, 14 MPa, 21 MPa, 28 MPa, 35 MPa, 42 MPa, 49 MPa, 56 MPa, 63 MPa and 70 MPa throughout the entire pressure range. Six measurements were performed at each eleven pressure points, three each in increasing and decreasing orders of pressures, respectively. Laboratories were advised to report the values of various parameters related to the artifact including the temperatures at which the measurements were made. As it was a digital gauge, all participating laboratories were requested to perform the measurement at a temperature sufficiently close to 23°C so that the standard uncertainty of the various coefficient of the artifact do not contribute to the overall measurement uncertainty. Data are analyzed as per ISO/IEC GUM document. The normalized error (En) values are estimated in the entire pressure range. These results are quite encouraging for the manufacturers and calibration laboratories that are facing a new environment after the WTO agreement.

PL

W pracy przedstawiono wyniki testowania (audytu) siedmiu laboratoriów akredytowanych przez Narodowy Komitet Akredytacyjny Laboratoriów w Indiach (NABL) z użyciem cyfrowego kalibratora ciśnienia DH Budenberg UK, jako artefaktu ciśnienia w zakresie 7-70 MPa.