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Question 1: Derive an expression for the shear stress at the pipe wall when an incompressible...
Please Show work Assume that the wall shear stress, Tw, created when a fluid flows through...
Please Show work
Assume that the wall shear stress, Tw, created when a fluid flows through a pipe (see Figure a) depends on the pipe diameter, D, the flowrate, Q, the fluid density, p, and the kinematic viscosity, U. Some model tests run in a laboratory using water in a 0.2-ft-diameter pipe yield the vs. Q data shown in Figure b. Perform a dimensional analysis and use model data to predict the wall shear stress in a 0.5-ft-diameter pipe through...
Starting from the expression for the flow rate in a pipe, Q. for incompressible fluid: Q=T...
Starting from the expression for the flow rate in a pipe, Q. for incompressible fluid: Q=T R* Ap /(8 uL) (1) where R is the pipe radius, Ap is the pressure difference between the inlet and the outlet sections. u is the fluid density, and L is the pipe length. please prove that: 4t/(0.5 p v)= 64 /Re (2) where tw is the wall shear stress, and p is the liquid density and v is the average velocity in the...
Question 3 [20 marks] Water (density p1000 kg/m2; dynamic viscosity 0.001 Pa-s) flows steadily through a horizontal, st...
Question 3 [20 marks] Water (density p1000 kg/m2; dynamic viscosity 0.001 Pa-s) flows steadily through a horizontal, straight pipe with circular cross section of diameter D=0.2 m. The volumetric flow rate is 0.01 m°/s. Argue that this is turbulent flow. [4 marksl а. Pressure drop in the pipe is due to friction. The pressure drop per unit length can be written as Др 4f L with U the average velocity in the pipe and fthe friction factor. Given the pipe...
fluid mechanics A steady, incompressible, and laminar flow of a fluid of viscosity u flows through...
fluid mechanics
A steady, incompressible, and laminar flow of a fluid of viscosity u flows through an inclined narrow gap of a crack in the wall of length L and a constant width W shown in Figure Q1(b). Assume that the gap has a constant thickness of 7. The fluid flows down the inclined gap at an angle and in the positive x-direction. No pressure gradient is applied throughout the flow but there is gravitational effect. Derive an expression for...
4. An incompressible fluid with viscosity u and density p was contained in pipe of length...
4. An incompressible fluid with viscosity u and density p was contained in pipe of length L and radius R. Initially the fluid is in rest. At t=0, a pressure difference of AP is applied across the pipe length which induces the fluid flow in axial direction (V2) Only varies with time (t) and pipe radius (r). There is no effect of gravity. To describe the fluid flow characteristics, after the pressure gradient is applied, answer the following questions: a)...
#1 Laminar Flow in Pipes The axial velocity in a pipe of radius R is given by, . Find the value o...
Fluid Mechanics
#1 Laminar Flow in Pipes The axial velocity in a pipe of radius R is given by, . Find the value of r (as a fraction of R) that maximizes u(r). How does this value of velocity compare with Vc? Compute the wall shear stress, du or Perform a control volume analysis on a pipe section of length e. Relate the pressure drop across the pipe section to the shear stress. Substitute the relation above for tw to...
Using dimensional analysis, express the characteristic length, velocity and time scales for near-wall flow in terms...
Using dimensional analysis, express the characteristic length, velocity and time scales for near-wall flow in terms of the density, viscosity and wall shear-stress. Show that the length scale can also be expressed as where v is the kinematic ur viscosity and u, is the friction velocity.
If the shear stress on the wall of a 30 cm pipe is 5 kg /...
If the shear stress on the wall of a 30 cm pipe is 5 kg / cm² and f = 0.04, what is the average velocity if water flows at 21 ° C and if oil of relative density 0.7 flows?
The laminar flow of a permanent incompressible Newtonian fluid in a long cylindrical pipe with a...
The laminar flow of a permanent incompressible Newtonian fluid in a long cylindrical pipe with a diameter D in vertical position is considered. Gravitational effects are taken into account, flow is carried out with a constant pressure gradient and gravity effect in the z- direction. a. Express the problem on the figure, write the given and accepted. b. Find the velocity profile in the fluid. c. Develop the relations that express the volumetric flow and shear stress in the pipe...
105. When an incompressible fluid flows steadily through a round pipe, the pressure drop AP due...
105. When an incompressible fluid flows steadily through a round pipe, the pressure drop AP due to friction is given by where ? is the fluid density, Vis the velocity, L/D is the pipe length-to- diameter ratio, and f is the D'Arcy friction coefficient. For laminar flow, the friction coefficient f can be related to the Reynolds number, Re, by a relationship of the form ??? Use the measured data in Table 5 to determine a and b by a...
Please Show work
Assume that the wall shear stress, Tw, created when a fluid flows through a pipe (see Figure a) depends on the pipe diameter, D, the flowrate, Q, the fluid density, p, and the kinematic viscosity, U. Some model tests run in a laboratory using water in a 0.2-ft-diameter pipe yield the vs. Q data shown in Figure b. Perform a dimensional analysis and use model data to predict the wall shear stress in a 0.5-ft-diameter pipe through...
Starting from the expression for the flow rate in a pipe, Q. for incompressible fluid: Q=T R* Ap /(8 uL) (1) where R is the pipe radius, Ap is the pressure difference between the inlet and the outlet sections. u is the fluid density, and L is the pipe length. please prove that: 4t/(0.5 p v)= 64 /Re (2) where tw is the wall shear stress, and p is the liquid density and v is the average velocity in the...
Question 3 [20 marks] Water (density p1000 kg/m2; dynamic viscosity 0.001 Pa-s) flows steadily through a horizontal, straight pipe with circular cross section of diameter D=0.2 m. The volumetric flow rate is 0.01 m°/s. Argue that this is turbulent flow. [4 marksl а. Pressure drop in the pipe is due to friction. The pressure drop per unit length can be written as Др 4f L with U the average velocity in the pipe and fthe friction factor. Given the pipe...
fluid mechanics
A steady, incompressible, and laminar flow of a fluid of viscosity u flows through an inclined narrow gap of a crack in the wall of length L and a constant width W shown in Figure Q1(b). Assume that the gap has a constant thickness of 7. The fluid flows down the inclined gap at an angle and in the positive x-direction. No pressure gradient is applied throughout the flow but there is gravitational effect. Derive an expression for...
4. An incompressible fluid with viscosity u and density p was contained in pipe of length L and radius R. Initially the fluid is in rest. At t=0, a pressure difference of AP is applied across the pipe length which induces the fluid flow in axial direction (V2) Only varies with time (t) and pipe radius (r). There is no effect of gravity. To describe the fluid flow characteristics, after the pressure gradient is applied, answer the following questions: a)...
Fluid Mechanics
#1 Laminar Flow in Pipes The axial velocity in a pipe of radius R is given by, . Find the value of r (as a fraction of R) that maximizes u(r). How does this value of velocity compare with Vc? Compute the wall shear stress, du or Perform a control volume analysis on a pipe section of length e. Relate the pressure drop across the pipe section to the shear stress. Substitute the relation above for tw to...
Using dimensional analysis, express the characteristic length, velocity and time scales for near-wall flow in terms of the density, viscosity and wall shear-stress. Show that the length scale can also be expressed as where v is the kinematic ur viscosity and u, is the friction velocity.
105. When an incompressible fluid flows steadily through a round pipe, the pressure drop AP due to friction is given by where ? is the fluid density, Vis the velocity, L/D is the pipe length-to- diameter ratio, and f is the D'Arcy friction coefficient. For laminar flow, the friction coefficient f can be related to the Reynolds number, Re, by a relationship of the form ??? Use the measured data in Table 5 to determine a and b by a...
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