a) The Stokes number, S, used in particle-dynamics studies is a dimenşionless combination of five variables: acceleration of graviy g, viscosity µ, density pe particle velocity U, and particle diameter D. If St is propotional to Aand inversely propotional to g, find its dimensionless form.
Q: 04: Use dimensional analysis to show that in a problem involving shallow water waves (Figure 1),…
A:
Q: 5.28 A simply supported beam of diameter D, length L, and modulus of elasticity E is subjected to a…
A: 1 We know Deflection depends on diameter,length,velocity,density,modulus of elasticity and…
Q: (a) Discuses three necessary conditions for complete similarity between a model and a prototype in…
A: a. A model and a prototype complete similarity is depicted by considering following three…
Q: The population P in thousands of Tallahassee, Florida, from 2000 through 2014 can be modeled by P =…
A: Given, P=150.9ekt Note: P is in thousands, which means if P=1, the population is 1000. a) At yeat…
Q: Important variables in a particular water machine are: Fluid density (ρ), impeller angular velocity…
A: Write the dimension of the variables used for the particular water machine.
Q: Use dimentional analysis to evaluate that in a problem involving shallow water waves (figure 6),…
A:
Q: 10) The shape of a rain drop falling in the athmosphere is given by the following formula developed…
A: given data
Q: From Fourrier's law, the rate of heat transfer in pl. is described by: Q = S(k,A,AT, x) where k =…
A: Given Data⇒ Fourier's law of heat transfer : Q=fk,A,∆T,x We want to use Buckingham's Pi theorem to…
Q: For studying of a dam in the laboratory, a model overflow has been built in the scale of , to 36…
A: (i) The scale ratio of the model to prototype is given as, The flow rate of the model is given as,…
Q: 1.16 Assume that the speed of sound, c, in a fluid depends on an elastic modulus, E, with dimensions…
A:
Q: 03: The power output (P) of a marine current turbine is assumed to be a function of velocity U,…
A: Solution: SInce number of variables is more than three, Buckingham π-theorem is more suitable for…
Q: 1- The pressure drop, Ap, along a straight pipe of diameter D has been experimentally studied, and…
A: Given, Pressure drop = ∆p Diameter = D Length = l Velocity = V Fluid viscosity = μ
Q: 1. In Buckingham n theorem, if n is the number of variables and m is the number of basic dimensions,…
A: 1) option A 2) option A
Q: The laminar pipe flow example of" design a capillary viscometer|. If Q is the volume flow rate, L is…
A: Write the given formula for viscosity of the fluid in the laminar pipe flow.
Q: Task 2 Evaluate the use of dimensionless analysis using the Buckingham Pi Theorem for a given fluid…
A:
Q: H. It is known that the total quantity within an exponential function [-0.1*t in the previous…
A: (H) The given function is Let the dimension of the constant be x. For the power of exponent…
Q: A rectangular block of height Land horizontal cross-sectional area A floats at the interface between…
A: Given data as per question The density of the first fluid = p1 g/cm3 The density of second fluid =p2…
Q: Check the following equation for dimensional homogeneity: mv = [" (Fcost) at where m is mass, v is…
A: Given data: m v = ∫t1t2 F cos θ dt Where m is mass , v is velocity,F is force, θ is angle, and t…
Q: Volumetric flow rate, Q, of a pump is a function of impeller diameter d, fluid velocity V, pressure…
A: (a). DIMENSIONAL FORMULAE given, volume flow rate=Q Q=[L3T-1] ,d=[L1] impeller diameter of pump=d…
Q: 03: The power output (P) of a marine current turbine is assumed to be a function of velocity U,…
A: In this question in the first part we have to prove the relation and in rest of the parts we need…
Q: Mott ." cometer, which we can analyze later in Chap. 7. A small ball of diameter D and density p,…
A: The data given is, The specific gravity of steel ball, SGb = 7.87 The diameter of the steel ball, D…
Q: Fluid mechanics theory The power input P to a centrifugal pump is a function of the volume flow Q,…
A:
Q: (d) The force, F, of a turbine generator is a function of density p, area A and velocity v. By…
A: d) The dimensions of the variables are given by,
Q: The thrust force of propeller (P) depends upon the flow velocity V, angular velocity o, diameter D,…
A: Diamensional analysis Dimensional analysis is a method of simplifying a physical problem by dividing…
Q: Measurements at a certain point of a pipe have been done where the following parameters were…
A: Ans: 30m
Q: 6. A pump's power P depends on rotational speed o, flow rate Q, fluid density p, and impeller…
A: a. To express Power in terms of density , discharge and diameter As we know that, P=ρgQHand HN2…
Q: Question 10) Important variables in a particular water machine are: Fluid density (p), impeller…
A: Write the dimension of the variables used for the particular water machine.
Q: Find the value of the following dimensionless group from the given data. a) The Froude number, NEr…
A: Solution:
Q: viscous torque T produced on a disc rotating in a liquid depends upon teristic dimension D, the…
A: Sfgh
Q: nvestigate with dimensional analysis, is this equation true t = [ 2x / a ]1/2 B. Express…
A:
Q: Kinetic energy of a fluid flow can be computed by pu - vdV, where p(r, y, z) and v(z,y, z) are the V…
A: Vector is a physical quantity that has magnitude and direction both. Scalar is a physical quantity…
Q: Pressure gages, such as the bourdon gage in Fig. , arecalibrated with a deadweight piston. If the…
A: Given Data: The total weight of the piston and weight is W = 44 N. The diameter of the neck is d =…
Q: The quantities viscosity µ, velocity V, and surface tension Y may be combined into a dimensionless…
A:
Q: A certain small river has an average width of 60 feet and a depth of 4 feet.This river carries water…
A: Froude number Fr =vgl
Q: Q1: Ah/L is the loss of pressure in meter per unit length through a pipe and it depends on velocity…
A: Δhl represent the loss of pressure per meter length of pipeΔhl =f(v,g,D,μ,ρ)alsof1(Δhl…
Q: Dynamic viscosity of fluid Density of fluid If X= , then the unit of X is =- O m?/kg O m/sec? O…
A: 1) The unit of dynamic viscosity, The unit of density, Note that the ratio of the dynamic…
Q: External Problem 2: Dimensional analysis and similarity The viscous torque T produced on a disc…
A: Given: A viscous torque produces on a disc rotating depend upon characteristics dimension D, the…
Q: When a fluid flows slowly past a vertical plate of height h and width b, pressure develops on the…
A:
Q: 2. Consider a large industrial fan where the input power, W, depends on the fan impeller diameter,…
A: given data input power, W, depends on the fan impeller diameter, D, fluid viscosity, u, fluid…
Q: Discharge, Q through a venturimeter depends on the following variable Inlet pipe diameter - D Throat…
A: π-Buckingham theorem: Given that variable Q is dependent upon given 5 variables, D, d, Δp, ρ, μ…
Q: Q/ complete the dimensional formula and SI units for table. US SI. No Physical Quantity Dimensional…
A:
Q: O The power, W, generated by a certain windmill design depends upon its diameter, D, the air…
A:
Q: |Newton's law of viscosity can be written as follows for constant density (p) fluids. Tzx = -v…
A: Given Data: Newton's law of viscosity is given as τzx=-νdvxρdz The dimension of the kinematic…
Q: c) When small aerosol particles move through air or water, the Reynolds number is very small (Re <…
A: For solution refer below images.
Q: The Stokes-Oseen formula for drag force on a sphere at low speed is given as D = 3dV +916V 2d2,…
A: (a) To find out the dimensions of the viscosity coefficient, Both the items on the right-hand side…
Q: A dimensional analysis is performed on the drag on a boat. When the effects of viscosity can be…
A:
Q: (a) The Stokes number, St, used in particle-dynamics studies is a dimensionless combination of five…
A: Since we are allowed to answer one question at a time. We’ll answer the first question since the…
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
- Ius A fluid flow situation depends on the Nelocity (V), the density several lineor dimension, 4shi, h2.pressure drep (DO > gravity (9) , Viscosity , Susface tension ). and bulk mo dulus of elasticity k. Apply dimen sional analysis. to these variables td A s*The Stokes number, St, used in particle dynamics studies,is a dimensionless combination of five variables: accelerationof gravity g , viscosity μ , density ρ , particle velocity U ,and particle diameter D . ( a ) If St is proportional to μand inversely proportional to g , find its form . ( b ) Showthat St is actually the quotient of two more traditionaldimensionless groups.Taylor number (Ta) is used here to describe the ratio between the inertia effect and the viscous effect. By applying Buckingham Pi's Theorem, determine an equation for Ta as a function of the radius of inner cylinder (r), cylinder tangential velocity (v), fluid dynamic viscosity (u), gap distance (L) and fluid density (p). Q4
- When a steady uniform stream flows over a circular cylinder, vortices are shed at a periodic rate. These are referred to as Kármán vortices. The frequency of vortex shedding få is defined by the free-stream speed V, fluid density p, fluid viscosity u, and cylinder diameter D. Use the Buckingham Pi method to show a dimensionless relationship for Kármán vortex shedding frequency is St = f (Re). Show all your work. V DHow can I use dimensional analysis to show that in this problem both Froude's number and Reynold's number are relevant dimensionless parameters? Problem: Here shallow waves move at speed c. The surface of the waves is a function depth (h), gravitational accelaration is g, densisty is p and fluid viscosity is μ. I need to get the parameter in the form in the image. Please help :)In the study of turbulent flow, turbulent viscous dissipation rate ? (rate of energy loss per unit mass) is known to be a function of length scale l and velocity scale u′ of the large-scale turbulent eddies. Using dimensional analysis (Buckingham pi and the method of repeating variables) and showing all of your work, generate an expression for ? as a function of l and u′.
- The Stokes number, St, used in particle-dynamics studies is a dimensionless combination of 5 variables: acceleration of gravity g, viscosity μ, density p, particle velocity U, and particle diameter D. If St is propotional to μ and inversely proportional to g, find its dimensionless form.The spin rate of a tennis ball determines the aerodynamic forces acting on it. In turn, the spin rate is a§ectedby the aerodynamic torque. If the torque depends on áight speed V , density , viscosity , ball diameter D,angular velocity !, and the fuzz height, hf , Önd the important dimensionless variables for this case. Use V ,, and D as your scaling (repeating) variables.During World War II, Sir Geoffrey Taylor, a British fluid dynamicist, used dimensional analysis to estimate theenergy released by an atomic bomb explosion. He assumed that the energy released E, was a function of blastwave radius R, air density ρ, and time t. Arrange these variables into single dimensionless group, which we mayterm the blast wave number.
- When a liquid in a beaker is stired, whirlpool will form and there will be an elevation difference h, between the center of the liquid surface and the rim of the liquid surface. Apply the method of repeating variables to generate a dimensional relationship for elevation difference (h), angular velocity (@) of the whirlpool, fluid density (p). gravitational acceleration (2), and radius (R) of the container. Take o. pand R as the repeating variables.Consider fully developed flow between two infinite parallel plates separated by distance h, with the top plate moving and the bottom plate stationary. The flow is steady, incompressible, and two-dimensional in the xy-plane. a) 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. b) Name the common dimensionless number formed in (a). Hint: modifying the dimensionless number if necessary.Q3: The power output (P) of a marine current turbine is assumed to be a function of velocity U, blade length L, angular velocity o, fluid density p and kinematic viscosity v. wL UL (a) Use dimensional analysis to show that, PU3L2 %3D (b) In a full-scale prototype the current velocity U = 2.0 m/s and the angular velocity is w = 15 rpm. A 1:10 scale laboratory model is to be tested in fluid of the same density with angular velocity o = 60 rpm. What velocity should be used in the model tests? (c) If the power output in the model tests is 200 W, what power output would be expected in the prototype?