When an object moves through a fluid, the fluid exerts a viscous force F on the...
When an object moves through a fluid, the fluid exerts a viscous force F on the object that tends to slow it down. For a small sphere of radius R, moving slowly with a speed v, the magnitude of the viscous force is given by Stokes, law, F = 6πηRv, where η is the viscosity of the fluid. (a) What is the viscous force on a sphere of radius R = 8.9 x 10-4 m falling through water (η = 1.00 x 10-3 Pa·s) when the sphere has a speed of 3.9 m/s? (b) The speed of the falling sphere increases until the viscous force balances the weight of the sphere. Thereafter, no net force acts on the sphere, and it falls with a constant speed called the "terminal speed." If the sphere has a mass of 1.5 x 10-5 kg, what is its terminal speed?
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When an object moves through a fluid, the fluid exerts a viscous
force F on the...
with A small particle of radius R and density p, moving at speed vin a viscous...
with A small particle of radius R and density p, moving at speed vin a viscous fluid of density dynamic viscosity n experiences a drag force given by Stokes' law F= 69Rv Find an expression for the terminal velocity of the particle as it falls through the fluid under the influence of gravity which includes Pp, pg, R, and n.
Hi, Can you check my answers? If they're incorrect, please include a picture of the correct...
Hi,
Can you check my answers? If they're incorrect, please include a
picture of the correct answer written out on a peice of paper.
Thanks!!
c. When a spherical object of radius r moves at velocity v in a viscous liquid, the object experi- ences a drag force given by Stokes' Law (Fd = 6πrv. η). Given the apparent weight of the object above, under what condition would the object be falling at "terminal velocity"? State the equation for this...
The average velocity < v > of a viscous fluid through a pipe is proportional to...
The average velocity < v > of a viscous fluid through a pipe is proportional to the drop in pressure ∆P, length L, radius of the pipe r, and viscosity of the fluid η (units: kg/m/s). Performing various experiments it has been determined that the velocity is directly proportional to the drop in pressure divided by the length. Determine the dependence of < v > on these quantities.
A stainless steel ball (radius rsphere = 0.3175 cm, density ρsphere = 7.866 g/cm3) falls through...
A stainless steel ball (radius rsphere = 0.3175 cm, density ρsphere = 7.866 g/cm3) falls through a viscous fluid (density ρfluid = 1.2 g/cm3) and quickly reaches terminal speed v. You measure the ball’s position as a function of time to find v. The ball is at positions y = 10 cm at time 2.402 and at position y = 5 cm at time 3.26. Calculate the viscosity η of the fluid in units of poise = g/(cm-s), using your...
2. For "sufficiently large" objects moving "sufficiently fast" through a fluid (i.e. for large Reynolds numbers),...
2. For "sufficiently large" objects moving "sufficiently fast" through a fluid (i.e. for large Reynolds numbers), the drag force on the object is proportional to the square of its ve- locity (quadratic drag). In this limit, we can ignore viscosity and argue this dependence from kinetic considerations. (a) (2 points) Suppose a sphere of radius R moves with speed v through a fluid with mass density ρ. In a small time interval dt, what is the mass m of fluid...
The drag force F acting on a spherical particle of diameter D falling slowly through a...
The drag force F acting on a spherical particle of diameter D falling slowly through a viscous fluid at velocity u is found to be influenced by the diameter D, velocity of fall u, and the viscosity . Using the method of dimensional analysis obtain a relationship between the variables. Number of variables is a. (5) Ob. (6) c. (7) d. None of the above Number of the dimensions is e. (3) f. (4) g. (5) Number of the groups...
A body falling in a relatively dense fluid, oil for example, is acted on by three...
A body falling in a relatively dense fluid, oil for example, is
acted on by three forces (see Figure 2.3.5): a resistive force R, a
buoyant force B, and its weight w due to gravity. The buoyant force
is equal to the weight of the fluid displaced by the object. For a
slowly moving spherical body of radius a, the resistive force is
given by Stokes's law, R = 6*pi*u*a*|v|, where v is the velocity of
the body, and u...
An object moving in a liquid experiences a linear drag force: D⃗ =(bv, direction opposite the...
An object moving in a liquid experiences a linear drag force: D⃗ =(bv, direction opposite the motion), where b is a constant called the drag coefficient. For a sphere of radius R, the drag constant can be computed as b=6πηR, where η is the viscosity of the liquid. Water at 20 ∘C has viscosity η=1.0×10−3Ns/m2. Suppose a 4.4-cm-diameter, 34 g ball is shot horizontally into a tank of 20 ∘C water. How long will it take for the horizontal speed...
organisms. If we have a sphere moving in a fluid of density ρ and viscosity μ,...
organisms. If we have a sphere moving in a fluid of density ρ and viscosity μ, and the sphere has a radius R and speed r and drag coefficient Co, then the drag and viscous forces are given by these equations: 2. in this problem, we'll estimate which resistive force- viscous force or drag force-dominates for two different The Reynolds number is given by Re ()Rv. For air and water, we can use the densities and viscosities in the table...
A fluid moves through a tube of length 1 meter and radius r=0.008 ± 0.00025 meters...
A fluid moves through a tube of length 1 meter and radius r=0.008 ± 0.00025 meters under a pressure p=4⋅10^5 ± 1500 pascals, at a rate v=0.875⋅10^−9 m^3 per unit time. Use differentials to estimate the maximum error in the viscosity η given by η=(π/8)(pr^4/v). maximum error ≈
with A small particle of radius R and density p, moving at speed vin a viscous fluid of density dynamic viscosity n experiences a drag force given by Stokes' law F= 69Rv Find an expression for the terminal velocity of the particle as it falls through the fluid under the influence of gravity which includes Pp, pg, R, and n.
Hi,
Can you check my answers? If they're incorrect, please include a
picture of the correct answer written out on a peice of paper.
Thanks!!
c. When a spherical object of radius r moves at velocity v in a viscous liquid, the object experi- ences a drag force given by Stokes' Law (Fd = 6πrv. η). Given the apparent weight of the object above, under what condition would the object be falling at "terminal velocity"? State the equation for this...
2. For "sufficiently large" objects moving "sufficiently fast" through a fluid (i.e. for large Reynolds numbers), the drag force on the object is proportional to the square of its ve- locity (quadratic drag). In this limit, we can ignore viscosity and argue this dependence from kinetic considerations. (a) (2 points) Suppose a sphere of radius R moves with speed v through a fluid with mass density ρ. In a small time interval dt, what is the mass m of fluid...
The drag force F acting on a spherical particle of diameter D falling slowly through a viscous fluid at velocity u is found to be influenced by the diameter D, velocity of fall u, and the viscosity . Using the method of dimensional analysis obtain a relationship between the variables. Number of variables is a. (5) Ob. (6) c. (7) d. None of the above Number of the dimensions is e. (3) f. (4) g. (5) Number of the groups...
A body falling in a relatively dense fluid, oil for example, is
acted on by three forces (see Figure 2.3.5): a resistive force R, a
buoyant force B, and its weight w due to gravity. The buoyant force
is equal to the weight of the fluid displaced by the object. For a
slowly moving spherical body of radius a, the resistive force is
given by Stokes's law, R = 6*pi*u*a*|v|, where v is the velocity of
the body, and u...
organisms. If we have a sphere moving in a fluid of density ρ and viscosity μ, and the sphere has a radius R and speed r and drag coefficient Co, then the drag and viscous forces are given by these equations: 2. in this problem, we'll estimate which resistive force- viscous force or drag force-dominates for two different The Reynolds number is given by Re ()Rv. For air and water, we can use the densities and viscosities in the table...
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