In this note the velocity field and the adequate shear stress corresponding to the unsteady flow of a frac- tional Maxwell fluid due to a constantly accelerating circular cylinder have been determined by means of the ...In this note the velocity field and the adequate shear stress corresponding to the unsteady flow of a frac- tional Maxwell fluid due to a constantly accelerating circular cylinder have been determined by means of the Laplace and finite Hankel transforms. The obtained solutions satisfy all imposed initial and boundary conditions. They can easily be reduced to give similar solutions for ordinary Maxwell and Newtonian fluids. Finally, the influence of pertinent param- eters on the fluid motion, as well as a comparison between models, is underlined by graphical illustrations.展开更多
The velocity field and the adequate shear stress corresponding to the longitudinal flow of a fractional second grade fluid,between two infinite coaxial circular cylinders,are determined by applying the Laplace and fin...The velocity field and the adequate shear stress corresponding to the longitudinal flow of a fractional second grade fluid,between two infinite coaxial circular cylinders,are determined by applying the Laplace and finite Hankel transforms.Initially the fluid is at rest,and at time t=0^+, the inner cylinder suddenly begins to translate along the common axis with constant acceleration. The solutions that have been obtained are presented in terms of generalized G functions.Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions.The corresponding solutions for ordinary second grade and Newtonian fluids are obtained as limiting cases of the general solutions.Finally,some characteristics of the motion,as well as the influences of the material and fractional parameters on the fluid motion and a comparison between models,are underlined by graphical illustrations.展开更多
have been done in the past by many researchers.Many factors which affect scour around piers such as shape of piers,size,positioning and orientation etc.have been studied in detail by them.However,similar studies in me...have been done in the past by many researchers.Many factors which affect scour around piers such as shape of piers,size,positioning and orientation etc.have been studied in detail by them.However,similar studies in meandering channels are scanty.Very few researchers have studied the effect of angular displacement which has considerable effects of scour around bridge piers.In this paper an attempt has been made to carry out a detailed study of angular displacement on scour.A constant diameter bridge pier of circular shape has been tested in a meandering channel bend with bend angle as 800.The test bed was prepared by using uniform sand having d50 as 0.27 mm and run was taken for a discharge of 2.5 l/s.展开更多
Spur dykes are the structures which are used to protect the eroding bank of rivers.They are sometimes also used to safeguard the life of many structures such as bridge piers,abutments etc.The efficiency of spur ...Spur dykes are the structures which are used to protect the eroding bank of rivers.They are sometimes also used to safeguard the life of many structures such as bridge piers,abutments etc.The efficiency of spur dykes has been checked in straight channels by conducting model tests in laboratories by many investigators.Very few studies were done in curved channels.In present work an attempt has been made to study the effect of location of spur dyke on bed and scour around bridge pier in curved open channel(bend angle=80o)with time.Experiment has been carried out in 80o channel bend at constant discharge(3.5×10^(-3) m^(3)/s)and bridge pier is located at angular displacementϴ=60o.Hereϴis the angle the line drawn at the inlet of any bend to the line joining the centre of curvature and any point on the outer portion of the bend.It is found that maximum scouring occurs atϴ=0o and 20oalong inner wall and atϴ=60o and 80o along outer wall.It is also found that scouring around bridge pier is more in the vicinity of pier and decreases with increase in distance from pier.The most suitable location for spur dyke to protect bridge pier is at angular displacementϴ=20o.Scour developed rapidly during initial time and then rate of scouring decreases with elapse of time.展开更多
文摘In this note the velocity field and the adequate shear stress corresponding to the unsteady flow of a frac- tional Maxwell fluid due to a constantly accelerating circular cylinder have been determined by means of the Laplace and finite Hankel transforms. The obtained solutions satisfy all imposed initial and boundary conditions. They can easily be reduced to give similar solutions for ordinary Maxwell and Newtonian fluids. Finally, the influence of pertinent param- eters on the fluid motion, as well as a comparison between models, is underlined by graphical illustrations.
文摘The velocity field and the adequate shear stress corresponding to the longitudinal flow of a fractional second grade fluid,between two infinite coaxial circular cylinders,are determined by applying the Laplace and finite Hankel transforms.Initially the fluid is at rest,and at time t=0^+, the inner cylinder suddenly begins to translate along the common axis with constant acceleration. The solutions that have been obtained are presented in terms of generalized G functions.Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions.The corresponding solutions for ordinary second grade and Newtonian fluids are obtained as limiting cases of the general solutions.Finally,some characteristics of the motion,as well as the influences of the material and fractional parameters on the fluid motion and a comparison between models,are underlined by graphical illustrations.
文摘have been done in the past by many researchers.Many factors which affect scour around piers such as shape of piers,size,positioning and orientation etc.have been studied in detail by them.However,similar studies in meandering channels are scanty.Very few researchers have studied the effect of angular displacement which has considerable effects of scour around bridge piers.In this paper an attempt has been made to carry out a detailed study of angular displacement on scour.A constant diameter bridge pier of circular shape has been tested in a meandering channel bend with bend angle as 800.The test bed was prepared by using uniform sand having d50 as 0.27 mm and run was taken for a discharge of 2.5 l/s.
文摘Spur dykes are the structures which are used to protect the eroding bank of rivers.They are sometimes also used to safeguard the life of many structures such as bridge piers,abutments etc.The efficiency of spur dykes has been checked in straight channels by conducting model tests in laboratories by many investigators.Very few studies were done in curved channels.In present work an attempt has been made to study the effect of location of spur dyke on bed and scour around bridge pier in curved open channel(bend angle=80o)with time.Experiment has been carried out in 80o channel bend at constant discharge(3.5×10^(-3) m^(3)/s)and bridge pier is located at angular displacementϴ=60o.Hereϴis the angle the line drawn at the inlet of any bend to the line joining the centre of curvature and any point on the outer portion of the bend.It is found that maximum scouring occurs atϴ=0o and 20oalong inner wall and atϴ=60o and 80o along outer wall.It is also found that scouring around bridge pier is more in the vicinity of pier and decreases with increase in distance from pier.The most suitable location for spur dyke to protect bridge pier is at angular displacementϴ=20o.Scour developed rapidly during initial time and then rate of scouring decreases with elapse of time.
