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Q2 (a) Derive an expression for the capillary-height change h, as shown, for a fluid of...
please show all your work! thanks A capillary tube with a radius of mm is inserted...
please show all your work! thanks
A capillary tube with a radius of mm is inserted vertically into a container of water. As shown in the picture at right, water wets the inner wall of the capillary with a contact angle of 0°. The surface tension force, Fst, (or capillary force in this context) draws water up the tube until the meniscus reaches a level of hw above the water level in the container. You may assume that surface tension...
The figure shows the effect of tube radius on the height to which capillary action can...
The figure shows the effect of tube radius on the height to which capillary action can raise a fluid. In this problem, assume the contact angle for water and glass is 0 degrees. The surface tension of water is .0728N/m Calculate the height, in meters, for water in a glass tube with a diameter of 1.7cm, a rather wide tube like the one on the left. What is the radius, in meters, of the glass tube on the right if...
(b) Figure Q2b shows two parallel plates with h apart, where an incompressible fluid is injected...
(b) Figure Q2b shows two parallel plates with h apart, where an incompressible fluid is injected into the tiny holes as shown. Assume total volume flow rate injected is Q and width of the plates is w. The fluid is only flowing horizontally between the two parallel plates. Gravitational force may be neglected. Obtain an expression for the pressure variation using the control volume method. Provide explanation as you show your steps. (29 marks) V(x) Pi Q Figure Q2b
M 13% Tools Q2 (B): For the water reservoir shown in figure, neglecting head losses and...
M 13% Tools Q2 (B): For the water reservoir shown in figure, neglecting head losses and surface tension effects, derive an equation for the water radius r in term of (Y/H). (20%) H 150 mm tre Water jet s 2 3 & 5 6 7 8 O W E R. Т. Y Р S D G K 4 cd
A biofluid is flowing down an inclined plane. The velocity profile of this fluid can be...
A biofluid is flowing down an inclined plane. The velocity profile of this fluid can be described by P& 2 Sine if the coordinate axis is aligned with the inclined plane. In the equation above, ρ and μ the fluid density and viscosity, respectively; g is the acceleration of gravity, h is the thickness of the fluid film, and θ is the angle of inclination of the plane. a. Sketch a diagram of the system and reference coordinates. (5 points)...
Problem 1: Differential Relations for a Fluid Particle (25 points) Two horizontal, infinite, parallel plates are...
Problem 1: Differential Relations for a Fluid Particle (25 points) Two horizontal, infinite, parallel plates are spaced a distance b apart. A viscous liquid is contained between the plates. The bottom plate is fixed, and the upper plate moves parallel to the bottom plate with a velocity U. Assume no-slip boundary conditions. There is no pressure gradient in the direction of flow (a) Demonstrate using the Navier-Stokes equation in the x-direction that the velocity profile is of the form: (15...
A rectangular plate of height h and base b feet is submerged vertically in a tank of fluid that weighs w pounds per cubi...
A rectangular plate of height h and base b feet is submerged vertically in a tank of fluid that weighs w pounds per cubic foot. The center of the plate is k feet below the surface of the liquid. The fluid force on the surface of the plate is given by F=wkhb. Find the fluid force on the rectangular plate given x=4 feet and y=5 feet.
A hill with the height h has the shape of a half circle as shown in...
A hill with the height h has the shape of a half circle as shown in figure below. The wind approaching the hill has a constant velocity parallel to the ground, U. Assume the stream function is in the form of ψ(r,0) = rn sin θ Find the value of n such that the flow is irrotational Use the surface (hill) streamline (ψ = 0) and the fact that at far field (r → stream function approaches to that of...
Consider a rectangular bar of thermal conductivity k W/m-K and total length 2L, as shown in...
Consider a rectangular bar of thermal conductivity k W/m-K and
total length 2L, as shown in the figure, is connected to a hot
surface that is at a temperature T1. The connection between the bar
and the surface is imperfect and results in a thermal contact
resistance of R’’ m2-K/W. The width of the rod into the depth of
the paper is W meters and the thickness of the rod is t meters. The
first section of the rod of...
1. An airplane if flying horizontally at a constant height of 6 km above a fixed observation poin...
1. An airplane if flying horizontally at a constant height of 6 km above a fixed observation point. At a certain moment the angle of elevation θ is 30° and decreasing and the speed of the plane is 4 km/h. (a) How fast is 0 decreasing at this moment? (b) How fast is the distance between the plane and the observation point is changing at this moment? 2. Trajectory of a particle is described by parametrical equations as t,y P,...
please show all your work! thanks
A capillary tube with a radius of mm is inserted vertically into a container of water. As shown in the picture at right, water wets the inner wall of the capillary with a contact angle of 0°. The surface tension force, Fst, (or capillary force in this context) draws water up the tube until the meniscus reaches a level of hw above the water level in the container. You may assume that surface tension...
(b) Figure Q2b shows two parallel plates with h apart, where an incompressible fluid is injected into the tiny holes as shown. Assume total volume flow rate injected is Q and width of the plates is w. The fluid is only flowing horizontally between the two parallel plates. Gravitational force may be neglected. Obtain an expression for the pressure variation using the control volume method. Provide explanation as you show your steps. (29 marks) V(x) Pi Q Figure Q2b
M 13% Tools Q2 (B): For the water reservoir shown in figure, neglecting head losses and surface tension effects, derive an equation for the water radius r in term of (Y/H). (20%) H 150 mm tre Water jet s 2 3 & 5 6 7 8 O W E R. Т. Y Р S D G K 4 cd
A biofluid is flowing down an inclined plane. The velocity profile of this fluid can be described by P& 2 Sine if the coordinate axis is aligned with the inclined plane. In the equation above, ρ and μ the fluid density and viscosity, respectively; g is the acceleration of gravity, h is the thickness of the fluid film, and θ is the angle of inclination of the plane. a. Sketch a diagram of the system and reference coordinates. (5 points)...
Problem 1: Differential Relations for a Fluid Particle (25 points) Two horizontal, infinite, parallel plates are spaced a distance b apart. A viscous liquid is contained between the plates. The bottom plate is fixed, and the upper plate moves parallel to the bottom plate with a velocity U. Assume no-slip boundary conditions. There is no pressure gradient in the direction of flow (a) Demonstrate using the Navier-Stokes equation in the x-direction that the velocity profile is of the form: (15...
A hill with the height h has the shape of a half circle as shown in figure below. The wind approaching the hill has a constant velocity parallel to the ground, U. Assume the stream function is in the form of ψ(r,0) = rn sin θ Find the value of n such that the flow is irrotational Use the surface (hill) streamline (ψ = 0) and the fact that at far field (r → stream function approaches to that of...
Consider a rectangular bar of thermal conductivity k W/m-K and
total length 2L, as shown in the figure, is connected to a hot
surface that is at a temperature T1. The connection between the bar
and the surface is imperfect and results in a thermal contact
resistance of R’’ m2-K/W. The width of the rod into the depth of
the paper is W meters and the thickness of the rod is t meters. The
first section of the rod of...
1. An airplane if flying horizontally at a constant height of 6 km above a fixed observation point. At a certain moment the angle of elevation θ is 30° and decreasing and the speed of the plane is 4 km/h. (a) How fast is 0 decreasing at this moment? (b) How fast is the distance between the plane and the observation point is changing at this moment? 2. Trajectory of a particle is described by parametrical equations as t,y P,...
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