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#1 Laminar Flow in Pipes The axial velocity in a pipe of radius R is given by, . Find the value o...
3. Water flowing through a pipe assumes a laminar-flow velocity profile at some section is parabolic:...
3. Water flowing through a pipe assumes a laminar-flow velocity profile at some section is parabolic: u(0) -4J Figure 2 where u(r) is the velocity at any position r, ß is a constant,-11s the viscosity of water, and r is the radial distance from the pipe centerline. (a) Develop an equation for u(r) assuming a parabolic velocity profile and using the known velocities at the walls u(ro)-0 and the center u(0) (Just use symbols). (b) Develop an equation for shear...
Problem The relation between pressure drop and flow rate of laminar flows in a pipe is given by l...
Problem The relation between pressure drop and flow rate of laminar flows in a pipe is given by l bar 50 m 20° 128u dz PS Flow rate Q is the product of the average velocity and the cross-sectional area of the pipe What is the pressure needed to drive a viscous oil flow upslope through a 12 cm diameter pipe? The length of the pipe is 50 meters. The slope is 20°. At the end of the pipe, the...
1. Some non-Newtonian fluids behave as a Bingham plastic for which shear stress can be expressed...
1. Some non-Newtonian fluids behave as a Bingham plastic for which shear stress can be expressed as + For laminar flow of a Bingham plastic in a horizontal pipe of radius R, the velocity profile is given as 4wr -R)+ (r-R), where AP/L is the constant pressure drop along the pipe per unit length, is the dynamic viscosity,r is the radial distance from the centerline, and is the yield stress of Bingham plastic. Develop a relation for (a) the shear...
2. (20 marks) The fully-developed, laminar fluid flow through a circular pipe is considered to be...
2. (20 marks) The fully-developed, laminar fluid flow through a circular pipe is considered to be one dimensional with a velocity profile given by u(r) = Umax(1 - 52/R2), where R is the radius of the pipe, r is the radial distance from the center of the pipe, and Umax is the maximum flow velocity at the center of the pipe. a) Derive a relation for the drag force applied by the fluid on a section of the pipe of...
Q5. Sketching a suitable control volume, show that the velocity profile V(r) for steady, fully laminar...
Q5. Sketching a suitable control volume, show that the velocity profile V(r) for steady, fully laminar flow in a horizontal pipe is given by V(r)- whereis is the pressure drop per unit length of pipe, R is the pipe radius and u the dynamic viscosity of the fluid. (10 marks) Thereafter develop Poiseuille's law for the volume flow rate O in the form SuL (10 marks) Hence show that the head loss h is given by where Vis the mean...
4. Consider upwards, laminar flow in a vertical pipe of length L. (a) Starting with the...
4. Consider upwards, laminar flow in a vertical pipe of length L. (a) Starting with the NS equations given in 6.128 c. simplify the eq'ns, state the BCs in the coordinate system shown, solve for vír), wall shear stress tw, and the average flow speed V=Q/rR; (b) rearrange your result into the form , like EB CV relation, (AP/pg +1)=f* (LD)V/(29) for arbitrary length L, and show that the friction factor f= C2/Rc and evaluate C2 as a number. Follow...
3. Water flowing through a pipe assumes a laminar-flow velocity profile at some section is parabolic: u(0) -4J Figure 2 where u(r) is the velocity at any position r, ß is a constant,-11s the viscosity of water, and r is the radial distance from the pipe centerline. (a) Develop an equation for u(r) assuming a parabolic velocity profile and using the known velocities at the walls u(ro)-0 and the center u(0) (Just use symbols). (b) Develop an equation for shear...
Problem The relation between pressure drop and flow rate of laminar flows in a pipe is given by l bar 50 m 20° 128u dz PS Flow rate Q is the product of the average velocity and the cross-sectional area of the pipe What is the pressure needed to drive a viscous oil flow upslope through a 12 cm diameter pipe? The length of the pipe is 50 meters. The slope is 20°. At the end of the pipe, the...
1. Some non-Newtonian fluids behave as a Bingham plastic for which shear stress can be expressed as + For laminar flow of a Bingham plastic in a horizontal pipe of radius R, the velocity profile is given as 4wr -R)+ (r-R), where AP/L is the constant pressure drop along the pipe per unit length, is the dynamic viscosity,r is the radial distance from the centerline, and is the yield stress of Bingham plastic. Develop a relation for (a) the shear...
2. (20 marks) The fully-developed, laminar fluid flow through a circular pipe is considered to be one dimensional with a velocity profile given by u(r) = Umax(1 - 52/R2), where R is the radius of the pipe, r is the radial distance from the center of the pipe, and Umax is the maximum flow velocity at the center of the pipe. a) Derive a relation for the drag force applied by the fluid on a section of the pipe of...
Q5. Sketching a suitable control volume, show that the velocity profile V(r) for steady, fully laminar flow in a horizontal pipe is given by V(r)- whereis is the pressure drop per unit length of pipe, R is the pipe radius and u the dynamic viscosity of the fluid. (10 marks) Thereafter develop Poiseuille's law for the volume flow rate O in the form SuL (10 marks) Hence show that the head loss h is given by where Vis the mean...
4. Consider upwards, laminar flow in a vertical pipe of length L. (a) Starting with the NS equations given in 6.128 c. simplify the eq'ns, state the BCs in the coordinate system shown, solve for vír), wall shear stress tw, and the average flow speed V=Q/rR; (b) rearrange your result into the form , like EB CV relation, (AP/pg +1)=f* (LD)V/(29) for arbitrary length L, and show that the friction factor f= C2/Rc and evaluate C2 as a number. Follow...
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