QUESTION 4 ,a) The Stokes number, S, used in particle-dynamics studies is a dimensionless combinationof five variables: acceleration of grayty g, viscosity 4, density pe particle velocity U, andparticle diameter D, If S, is propotional to Aanddinversely propotional to g, find itsdimensionless form.

Answered: Image /qna-images/answer/47623168-722e-436f-820a-80d6d64a81c7.jpg

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.

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.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: 5: The discharge pressure (P) of a gear pump (Fig. 3) is a function of flow rate (Q), gear diameter…

A: Here, pressure is a function of... P=f(Q,D,μ,ω)So, it can be written as,f1(P,Q,D,μ,ω)=0Here, total…

Q: The equation, given below, is describing the motion of the fluid in a pipe. The driving force of the…

A: To solve this problem, we need to apply the process of nondimensionalization to the given equation.…

Q: cording to the web site USGS Daily Water Data for the Nation, the mean flow rate in the New River…

Q: Let us model a certain cargo ship as a rectangular prism with length (100 m) and width (20 m). Also,…

A: We have to find 1.boat weight 2.how far below the waterline will the bottom of the boat be?

Q: At low velocities (laminar flow), the volume flow Q through a small-bore tube is a function only of…

A: Given: As stated in the question description, we can express the volume flow rate Q as,…

Q: Independent variables in a turbomachine are the impeller diameter, D, angular speed, ω, and fluid…

A: To perform dimensionless analysis, we use Bukingham's Pi theorem:If we have n variables and k…

Q: What are the primary dimensions of the following parameters: Energy, E; Specific energy, energy per…

Q: Write the primary dimensions of each of the following variables from the field of solid mechanics,…

A: Part (a) Moment of inertia (I) can be expressed as, Where, ri is the perpendicular distance of the…

Q: The velocity of propagation of ripples on the surface of a shallow liquid depends on the…

Q: The force, F, acting on a billboard due to wind depends on it length, l, height, h, the modulus of…

A: As it is given in the question that the force (F) depends in l, h, E, and γa. Here are the…

Q: 4. The water velocity at a certain point along a 1:10 scale model of a dam spillway is 5 m/s. What…

A: Velocity of prototype Vp=15.8m/sExplanation:

Q: Strain Stress Surface tension Temperature Time Torque Velocity Viscosity (dynamic) Viscosity…

Q: 5. The drag force, fd, on a sphere located in a pipe through which a fluid is flowing is to be…

A: The objective of the question is to determine the drag force on a sphere located in a pipe through…

Q: 5. Use dimensional analysis to estimate quantities. Consider a gas with density p, pressure p, and…

A: Consider the function of velocity in terms of independent properties.From the independent variables,…

Q: Derive two dimensionless parameters for the shear stress at the pipe wall when an incompressible…

Q: The speed of sound c in an ideal gas is known to be a function of the ratio of specific heats k,…

A: To determine: develop a functional relationship between the given parameters. There are a total of…

Q: Problem 1: Streamlining From dimensional analysis, we know the drag force is FD = CopAV²/2, where CD…

Q: Here, a 1:10 scale prototype of a propeller on a ship is to be tested in a water channel. What would…

Q: An airplane wing model is designed with a similarity test. The lift force is a function of speed,…

Q: Problem 1: The discharge pressure (P) of a centrifugal pump shown below is a function of flow rate…

A: Dimensions of given quantities will be, P=ML-1T-2Q=L3D=Lρ=ML-3ω=T-1 Thus, here basic dimension is 3…

Q: Problem 1 AUS In The power required to drive a propeller, P, is a found to be a function of the…

Question

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Problem 5 s): The discharge pressure (P) of a screw pump (Fig. 5) is a function of flow rate (Q), screw diameter (D), fluid viscosity (u) and screw angular speed (w). P = f (Q, D, μ, w). Use the pi theorem to rewrite this function in terms of dimensionless parameters, ₁ g (T₂). Choose Q, D, and u as repeating variables. Screw Fig. 5: Screw pump
Which of the following dimensionless parameters is the correct arrangement of the given parameters? (select all that O a. Pi = (Dp)/(Rho*V) Dp: Pressure change Rho: Density V: Velocity O b. Pi = (V*L*(Rho))/(nu) V: Velocity L: length Rho: Density nu: Dynamic viscosity O. Pi = Q/((A^1.5)*w) Q: Volumetric discharge rate A: Area w: Angular velocity O d. Pi = (a)(t^2)/(L) L: length a: acceleration t time
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.
Consider a boundary layer growing along a thin flat plate. The boundary layer thickness & at a downstream distance x is a function of x, the fluid density p, dynamic viscosity, and free stream velocity V. Use Buckingham's theorem with p, x and V as repeating variables, to obtain the relationship between dimensionless parameters Is. Figure 3.2
2. The apparatus shown below is designed to measure the density of an unknown fluid (p2₂). The two sides of the device are separated by a movable, frictionless partition. The partition is attached to the immobile sidewalls of the device via springs (different spring constants) on either side. Before pouring fluid into the device, both springs are unstretched. The device has a rectangular cross-section and extends a width w into the page. Derive an expression for the unknown density p2 = f(p1, h₁, h₂, k₁, k2, Ax, g), where Ar is the displacement of the partition relative to its equilibrium location before the fluids are poured into the apparatus. h₁ P1 k₁ 5 P2 ли Ax k₂ h₂
A dimensional analysis is performed on the drag on a boat. When the effects of viscosity can be neglected, the Euler number based on the drag D experienced by the boat is a function of a Froude number. The effects of the dimensions of the boat can be represented by its length I. The drag on a model of the model is measured as 0.35N. If the ratio of / for a full-scale model to the value of/ for the model is 46, calculate the expected drag on the full-scale boat. Your answer should be to the nearest kN. The properties of the water in the model test matches those for the full-scale boat.