generate a dimensionless relationship
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Q: The height H that fluid rises in a liquid barometer tubedepends upon the liquid density ρ , the…
A: Consider a function Express each of these dimensional variables in their dimensional form,
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A: Write the dimensions of the given parameters.
Q: Example: The pressure difference (Ap) between two point in a pipe due to turbulent flow depends on…
A: ∆P=fV, D, μ, ρ ,e, L
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Q: The radius R of a mushroom cloud generated by a nuclear bomb grows in time. We expect that R is a…
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Q: Use the method of repeating variables to find out the non-dimensional groups for the problem of fan…
A: To find: The non dimension group . Given: The power is function of p=f(D,ρ,ω,Q). Here, P is power, D…
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A: The drag coefficient will affect by parameters.
Q: The output power W. of a spinning shaft is a function of torque T and angular velocity ? . Use…
A: Given Data: The torque acting on the shaft is The angular velocity of the shaft is ω. The output…
Q: Q2: The power input P to a centrifugal pump is assumed to be a function of the volume flow Q,…
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Q: The following rheological data were collected on a new "Thick 'n Spicy" brand of tomato catsup at…
A: shear stress vs rate of shear is plotted which gives linear relation.
Q: In a steady-state bakery process, cakes are fed on a conveyor belt through an “enrober" where melted…
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Q: Consider laminar flow over a flat plate. The boundary layer thickness & grows with distance x down…
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Q: 1. Explain the three necessary conditions which must be met in order to achieve complete similarity…
A: The necessary condition which must be met in order to achieve similarity between a model and a…
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A: Dimensional analysis is used for?
Q: Derive an expression for the shear stress at the pipe wall when an incompressible fluid flows…
A: Write the dimension of the variables. Here, the number of variables is 5 and the number of…
Q: Q2: The power input P to a centrifugal pump is assumed to be a function of the volume flow Q,…
A: given :- The power input P to a centrifugal pump is assumed to be a function of the volume flow Q,…
Q: An oil film drains steadily down the side of a vertical wall, as shown on figure below. After an…
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Q: Take the full-blown Couette flow as shown in the figure. While the upper plate is moving and the…
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Q: The Stokes number, St, used in particle dynamics studies,is a dimensionless combination of five…
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Q: Q3: The power output (P) of a marine current turbine is assumed to be a function of velocity U,…
A: Given that The power output (P) of a marine current turbine is assumed to be a function of velocity…
Q: Consider a boundary layer growing along a thin flat plate. This problem involves the following…
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Q: Derive an expression for the shear stress at the pipe wall when an incompressible fluid flows…
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Q: The time t d to drain a liquid from a hole in the bottom of atank is a function of the hole…
A: Given data td=drain timed=hole diameteryo=initial fluid vol.ho=Liquid depthρ=density of…
Q: 7.4 Consider a disk of radius R rotating in an incompressible fluid at a speed w. The equations that…
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Q: The drag FD of the golf ball is affected by the speed V of the ball, the diameter d of the ball, the…
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Q: In a steady-state bakery process, cakes are fed on a conveyor belt through an “enrober" where melted…
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Q: Determine drag on the sphere for flow past a sphere (see the figure below) using these parameters D…
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Q: Select a common dimensionless parameter in fluid mechanics from the following: (a) angular…
A: Given options and To find the dimensionless parameter in fluid mechanics.
Q: Consider liquid flow of density ρ , viscosity μ , and velocityU over a very small model spillway of…
A: Let, Density of the liquid = ρ Dynamic viscosity = μ Velocity of flow = U Model length = L Surface…
Q: Consider laminar flow over a flat plate. The boundary layer thickness & grows with distance x down…
A: Solution: Mathematically, boundary layer thickness can be defined as δ=f(x,U,µ,ρ), it can be written…
Q: The thrust F of a propeller is generally thought to be afunction of its diameter D and angular…
A: The thrust force is the function of F=fD,ω,V,μ,ρ here n=6m=3 Now the replacing variables are μ,V,D…
Q: By dimensional analysis, obtain an expression for the drag force (F) on a partially submerged body…
A: Given Force = F Velocity = u Length = L Roughness = e Density of fluid = p Gravitational…
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Q: 2. 21 If there are n variables in a particular flow situation, and these variables contain in…
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Q: During World War II, Sir Geoffrey Taylor, a British fluid dynamicist, used dimensional analysis to…
A: Dimension analysis is the method of establishing a relationship between different physical…
Q: The pressure coefficient is defined by the ratio between the static pressure difference and the…
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Q: Volumetric strain rate is zero for a steady incompressible flow. In Cartesian coordinates we express…
A: In order to proceed with the problem some assumptions need to be taken into consideration. The flow…
Q: Q2/ By using the power series method make a dimensional analysis for the following variables: The…
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Q: Question (1): (A) The pressure difference Ap of air that flows through a fan, as shown in Figure…
A: Use Buckingham pi theorem to approach this problem,
Q: During World War II, Sir Geoffrey Taylor, a British fl uiddynamicist, used dimensional analysis to…
A: Given data: E = f (R, ρ, t ) where R = blast wave radius , E = energy released, ρ = air density,…
Use the first principle (dimensional analysis) to generate a dimensionless relationship for the x-component of fluid velocity u as a function of fluid viscosity μ, top plate speed v, distance h, fluid density ρ, and distance y.
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- By dimensional analysis, obtain an expression for the drag force (F) on a partially submerged body moving with a relative velocity (u) in a fluid; the other variables being the linear dimension (L), surface roughness (e), fluid density (p), and gravitational acceleration (g).The output power W. of a spinning shaft is a function of torque T and angular velocity ? . Use dimensional analysis to express the relationship between W., T, and ? in dimensionless form. Compare your result to what you know from physics and discuss brieflyThe thrust F of a propeller is generally thought to be afunction of its diameter D and angular velocity V , the forwardspeed V , and the density ρ and viscosity μ of the fl uid.Rewrite this relationship as a dimensionless function.
- During World War II, Sir Geoffrey Taylor, a British fl uiddynamicist, used dimensional analysis to estimate theenergy released by an atomic bomb explosion. He assumedthat the energy released E , was a function of blast waveradius R , air density ρ, and time t . Arrange these variablesinto a single dimensionless group, which we may term theblast wave number .3- Consider laminar flow over a flat plate. The boundary layer thickness & grows with distance x down the plate and is also a function of free-stream velocity U, fluid viscosity u, and fluid density p. Find the dimensionless parameters for this problem, being sure to rearrange if necessary to agree with the standard dimensionless groups in fluid mechanics.Using primary dimensions, verify that the Rayleigh number is indeed dimensionless. What other established nondimensional parameter is formed by the ratio of Ra and Gr?
- 1) When doing the dimensional analysis, the model fluid should be the same with prototype fluid. True or False 2) What is the unit of Reynolds number (Re)? a) Dimensionless b) m/s c) m2/s d) m/s2The height H that fluid rises in a liquid barometer tubedepends upon the liquid density ρ , the barometric pressurep , and the acceleration of gravity g . (a) Arrange these fourvariables into a single dimensionless group. (b) Can youdeduce (or guess) the numerical value of your group?An automobile has a characteristic length and area of 8 ft and 60 ft2, respectively. When tested in sea-level standard air, it has measured velocities of 20, 40, and 60 mi/h and drag forces of 31, 115, and 249 lbf, respectively. The same car travels in Colorado at 115 mi/h at an altitude of 3500 m. Using dimensional analysis, estimate its drag force (in lbf). Using dimensional analysis, estimate the horsepower required to overcome air drag (in hp)
- The time t d to drain a liquid from a hole in the bottom of atank is a function of the hole diameter d , the initial fluidvolume y 0 , the initial liquid depth h 0 , and the density ρ andviscosity μ of the fluid. Rewrite this relation as a dimensionlessfunction, using Ipsen’s method.The radius R of a mushroom cloud generated by a nuclear bomb grows in time. We expect that R is a function of time t, initial energy of the explosion E, and average air density ? . Use dimensional analysis to express the relationship between R, t, E, and ? in dimensionless form.Dimensional analysis is to be used to correlate data on bubble size with the properties of the liquid when gas bubbles are formed by a gas issuing from a small orifice below the liquid surface. Assume that the significant variables are bubble diameter D, orifice diameter d, liquid density rho, surface tension sigma (in N/m), liquid viscosity mu, and g. Select d, rho, and g as the core variables.