The Flow Rate Equation of Granular Materials from Pyramidal Hoppers

Abstract This paper presents a novel hydrostatic actuator, which is named as linear-driven electro-hydrostatic actuator (LEHA). In an LEHA, the actuator is driven by a novel collaborative rectification pump (CRP), which incorporates two miniature cylinders and two spool valves. Specifically, the CRP is driven by two linear oscillating motors, which are designed and optimized to generate reciprocating motion at high frequency with adequate stroke. CRP offers a highly novel linear fluid pump with flexibility in bi-directionally driving. In this paper, schematic of LEHA is first presented and its kinematic flow rate equation is derived. Then the design of CRP, linear oscillating motor, as well as the whole LEHA prototype is introduced. Performance of the LEHA is demonstrated through a series of experiments and simulation, and analysis of the results is also included.

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Relation Between the Flow-Rate Equation and Length of Converging Section of Parshall Flume

Transactions of the ASAE ◽

10.13031/2013.41127 ◽

1960 ◽

Vol 3 (2) ◽

pp. 0086-0088

Author(s):

Victor L. Hauser

Keyword(s):

Flow Rate ◽

Rate Equation

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The pressure drop/flow rate equation for non-Newtonian flow in channels of irregular cross-section

Polymer Engineering & Science ◽

10.1002/pen.760282306 ◽

1988 ◽

Vol 28 (23) ◽

pp. 1559-1564 ◽

Cited By ~ 10

Author(s):

Ta-Jo Liu ◽

Chin-Nan Hong

Keyword(s):

Pressure Drop ◽

Cross Section ◽

Flow Rate ◽

Rate Equation ◽

Newtonian Flow ◽

Drop Flow

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Optimization of Granular Chute Flow with Two Bottlenecks

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.487.532 ◽

2014 ◽

Vol 487 ◽

pp. 532-535 ◽

Cited By ~ 1

Author(s):

Qi Yi Liu ◽

Guo Cheng Yang ◽

Mao Bin Hu ◽

Rui Jiang ◽

Qing Song Wu ◽

...

Keyword(s):

Flow Pattern ◽

Granular Materials ◽

Flow Rate ◽

Transition Point ◽

Flow Transition ◽

Chute Flow ◽

Dense Flow ◽

Bistable Phenomenon ◽

Industrial Mining ◽

Pharmaceutical Processes

Granular materials are ubiquitous in industrial, mining and pharmaceutical processes. In this paper, we study the flow pattern and optimization of granular chute flow with two bottlenecks. The dependence of flux on channel width show dilute to dense flow transition. A remarkable bistable phenomenon appears near the transition point. Base on this discovery, one can optimize the flow rate along such channels.

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A flow rate equation for subsonic Fanno flow

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406213480295 ◽

2013 ◽

Vol 227 (12) ◽

pp. 2724-2729 ◽

Cited By ~ 4

Author(s):

Eizo Urata

Keyword(s):

Mass Flow Rate ◽

Mass Flow ◽

Flow Rate ◽

Rate Equation ◽

Degrees Of Freedom ◽

Relative Difference ◽

State Variables ◽

Mass Flow Rates ◽

Proper Values ◽

The Given

The aim of this note is to obtain a flow rate equation for subsonic Fanno flow, which has a form similar to the flow rate equation for isothermal flow. When pipe dimensions and the proper values of pressures and temperatures at two sections along a pipe, namely P1, P2, T1 and T2 are given, the mass flow rate is obtained by simple substitution into the obtained formula. However, only three of the above four quantities are independently given, since the steady Fanno flow problem involves three first-order differential equations. Therefore, the problem has three degrees of freedom. The theory in this note shows an algebraic equation that determines the fourth quantity by using the given three quantities. The method for finding the mass flow rate and state variables of the gas in the pipe are substantially simplified compared with the commonly distributed method. The relative difference of mass flow rates between the subsonic Fanno and isothermal flows is smaller than 1% in practical combinations of P2 /P1 and the pipe-friction parameter fL/D.

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Gravity Flow of Granular Materials in Conical Hoppers

Journal of Applied Mechanics ◽

10.1115/1.3424601 ◽

1979 ◽

Vol 46 (3) ◽

pp. 529-535 ◽

Cited By ~ 45

Author(s):

T. V. Nguyen ◽

C. Brennen ◽

R. H. Sabersky

Keyword(s):

Experimental Data ◽

Approximate Solution ◽

Granular Material ◽

Granular Materials ◽

Flow Rate ◽

Yield Condition ◽

Wall Stress ◽

Perfectly Plastic ◽

Analytical Expressions ◽

Conical Hopper

An approximate solution to the flow of a cohesionless granular material in a conical hopper is presented. The material is modeled as a perfectly plastic continuum which satisfies the Mohr-Coulomb yield condition. Analytical expressions of the mass flow rate and the wall stress are derived and compared to some experimental data and other analyses.

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