The resistance R, to the motion of a completely submerged body depends upon the length of the body L, velocity of flow V, mass density of fluid p and kinematic viscosity of fluid v. By dimensional analysis prove that VL R = pV?1

The resistance R, to the motion of a completely submerged body depends upon the length of the body L, velocity of flow V, mass density of fluid p and kinematic viscosity of fluid v. By dimensional analysis prove that VL R = pV?1

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.13P: 5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its...

See similar textbooks

Related questions

Q: The Power (P) required to drive the pump depends upon the diameter (D), the angular velocity (@),…

A: Total variable =P,D,ω,Q,ρ P= f(D,ω,Q,ρ) where P is a dependent variable

Q: A catheter-sensor system for invasive pressure measurements has a catheter with a length of 1 m and…

Q: Q2) A) Apply the principle of dimensional analysis to the problem of a screw propeller and assume…

Q: An incompressible fluid (kinematic viscosity, 7.4 x10-7 m2/s, specific gravity, 0.88) is held…

Q: Books on porous media and atomization claim that the viscosityμ and surface tension Y of a fl uid…

A: Let us consider an arbitrary constant K that depends upon the dynamic viscosity, surface tension and…

Q: of relative density 0.8. If the tank is given a horizontal acceleration of 10 m/s2, calculate The m

Q: Q3: The power output (P) of a marine current turbine is assumed to be a function of velocity U,…

Q: The resistance (R) experienced by a partially submerged body depends upon the velocity (u), length…

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

Q: 1. Consider a gas atmosphere with pressure distribution p(z) = po (1 – 2 tan'(z/H)) where z is the…

A: The pressure distribution is given by,

Q: The thrust P of a propeller depends upon diameter (D); speed (u) through a fluid density (p);…

A: Given data: P = f (D,u,N,ρ,μ) To determine: The above mentioned non-dimensional correlation

Q: Potide Use Buckingham's Pi Theorem to determine non-dimensional parameters in the phenomenon shown…

A: Variables are ∆P, R, σs.

Q: A large open tank is open to sea-level atmosphere and fi lledwith liquid, at 20 ° C, to a depth of…

A: Write the value of atmospheric pressure at the given temperature i.e. 20 oC. Here, patm is the…

Q: A square block weighing 1.1 KN and 250 mm on an edge slides down an 20 degrees inclined on a film of…

Q: Consider a soap bubble of diameter 3 mm. If the surface tension coefficient is 0.072 N/m and…

A: Given Data diameter=3mm radius =1.5mm=0.0015m P0=0Kpa σ=0.072 N/m

Q: Q2:- If the velocity of flow v, dynamic viscosity u, bulk modulus of elasticity K and diameter of…

Q: Q2:- If the velocity of flow v, dynamic viscosity a, bulk modulus of elasticity K and diameter of…

A: ,

Q: The absolute viscosity μ of a fluid is primarily afunction of( a ) Density, ( b ) Temperature, ( c )…

A: The term viscosity can be defined simply as resistance to flow. In fluid mechanics, it is the…

Q: The Reynold's number of a sphere falling in air is 1E6. If the sphere's radius is 1ft, what is its…

A: Given data: The Reynold’s number of a sphere falling in air, Re=1E6=1×106 The sphere’s radius, r=1…

Q: Taylor number (Ta) is used here to describe the ratio between the inertia effect and the viscous…

A: Solution: Taylor number depends upon (i) inner radius (r) (ii) cylinder tangential velocity (v)…

Q: The viscous torque T produced on a disc rotating in a liquid depends upon the characteristic…

A: T-TorqueD-DiameterN-Rotation Speedδ-Densityμ-Dynamic Viscosity

Q: Q3: An infinite plate is moved over a second plate on a layer of liquid as shown in figue (4) .For…

A: Note- As per our company's guidelines we are allowed to answer only first three subparts. kindly…

Q: Q1: If an air stream flowing at velocity (U) pasta body of length (L) causes a drag force (F) on the…

A: Force is dependent on the body U,L and fluid viscosity μ Now, we write the dimension formulae of…

Q: The pressure drop (Ap) test is carried out using a pipe configuration as illustrated below:…

Q: Q (3):-Pressure equal to 5. 16x104 N/m2 and temperature equal to 213.8 K at flying point ? what is…

A: We have to determine altitude and density

Q: Q2 :-If the velocity of flow over surface v, Surface tension o, density of flowp length of surface…

Q: Q1) Under laminar conditions, the volume flow rate Q through a small triangular-section pore of side…

Q: A model submarine with a length of T = 6.0 m is to be tested in a laboratory wind tunnel using air.…

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…

Q: Turbine An aircraft pulls a banner as shown below. The aircraft speed is 144 km/h. The banner is 25…

A: Write the given data. v=144 km/h=144 km/h518=40 m/sl=25 mh=4 mρ=1.2 kg/m3ν=1.6×10-5 m2/s

Q: The pressure coefficient is defined by the ratio between the static pressure difference and the…

Q: The density of a fluid is given by the empirical equation: ? = 70.5exp(8.27×10^−7 ?), where ? is…

Q: a1/ The power of 6-blade flat blade turbine agitator in a tank is a function of diameter of…

A: Given :- The power of 6-blade flat blade turbine agitator in a tank is a function of diameter of…

Q: An incompressible fluid (kinematic viscosity, 7.4 x10-7 m²/s, specific gravity, 0.88) is held…

A: Given: The kinematic viscosity of fluid = 7.4x10-7 m2/s The specific gravity = 0.88 The speed of top…

Q: Viscosity can be measured by flow through a thin-bore or capillary tube if the flow rate is low. For…

A: The diameter of the pipe is D=2 mm. The pressure drop is ∆p=5 kPa. The length of the tube is L=1 m.…

Q: Q1. Given the following system, find the shear stress in kg/m², developed on the fixed plate. The…

Q: The efficiency (n) of a fan depends upon density (p), and dynamic viscosity (µ) of the fluid,…

Q: 8. The density of air is about 1.24kg/m³ at sea level and virtually zero at upper levels of the…

Q: For most gases at standard or near standard conditions, the relationshipamong pressure, density, and…

A: Given: The value of R is R=287 J/kg∙K=1716 ft∙lb/slug∙⁰R. Part (a) The expression for the perfect…

Q: (Dimensional Analysis) If the velocity V in a fluid flow depends on a dimension 1, the fluid density…

Q: Which one is not a fundamental type of motion or deformation an element may undergo in fluid…

A: Rotation is not a fundamental type of motion or deformation an element may undergo in fluid…

Q: The pilot of a Boeing 767 determines that a total of 22,300 kilograms of jet fuel is needed to fly…

A: Sol.- Given: Total jet fuel needed to fly from Montreal to Edmonton = 22300 kg Volume of jet fuel…

Q: The kinematic viscosity of liquid oil is 20 stoke and relative density = 0.85. Find the dynamic…

A: Given: kinematic viscosity of liquid = 20 stokes The relative density = 0.85

Q: The drag force acting on a model torpedo, 1/20 the size of the prototype, is measured at 80 N in…

A: F= cd 12ρ A V2 cd = coeff of drag ρ = density A = reference areaV = velocity

Q: Directions: Solve the following problems completely, and make a detailed solution. Any incomplete…

Q: A flow from an injector is leading to the formation of a spray of liquid drops. The drops formed in…

Q: 1 (a) A plate 0.05mm distant from a fixed plate moves at 1.15 m/s and required a force per unit area…

Concept explainers

Properties of Fluids

The term fluid represents a type of substance that can easily change its shape under any external pressure/force and can flow. Fluids can acquire any shape in which it is stored and can resist normal stresses but cannot resist shear stress in rest condition. Whenever external shear stress is applied to fluids, it starts to flow. The fluids may be liquid or gas. Example- water, air, etc.

Question

The resistance R, to the motion of a completely
submerged body depends upon the length of
the body L, velocity of flow V, mass density of
fluid p and kinematic viscosity of fluid v. By
dimensional analysis prove that
R = pr* L')
VL'
= pV?1

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

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 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

The absolute viscosity μ of a fluid is primarily afunction of( a ) Density, ( b ) Temperature, ( c ) Pressure, ( d ) Velocity,( e ) Surface tension
The Reynolds number for a 1-ft-diameter sphere moving at2.3 mi/h through seawater (specifi c gravity 1.027, viscosity1.07 E-3 N ? s/m 2 ) is approximately( a ) 300, ( b ) 3000, ( c ) 30,000, ( d ) 300,000, ( e ) 3,000,000
The volume flow in a water pipe is 9000 m°/h. The pipe length is 80 m, the pipe diameter 1 m. The material data of water are a density of 1000 kg/m? and kinematic viscosity v=10® m7s. A steel pipe with roughness 0.05 mm is used. Determine the pressure drop in the pipe.
An oil has a kinematic viscosity of 1.25 E-4 m 2 /s and aspecifi c gravity of 0.80. What is its dynamic (absolute)viscosity in kg/(m ∙ s)?( a ) 0.08, ( b ) 0.10, ( c ) 0.125, ( d ) 1.0, ( e ) 1.25
A square block weighing 1.1 KN and 250 mm on an edge slides down an 20 degrees inclined on a film of oil 6.0 micrometer thick. Assuming a linear velocity profile in the oil, what is the terminal speed of the block in m/s. The viscosity of the oil is 7 mPa-s. a.5.16 b.5.62 c.5.75 d.5.48
In the gap between the two plates, the lubricant flows in one direction (x) by the pressure gradient. Lubricants are incompressible Newtonian fluids, flows are laminates, and terminal effects are ignored. Find the maximum flow rate [m/s] when the pressure difference (△P/L) per unit length is 25000 Pa/m.Data: clearance between plates (B) = 6 mm, lubricant viscosity (μ) = 25 cP (1cP = 10-3 Pa·s), lubricant density (=) = 0.88 g/cm3
In the gap between the two plates, the lubricant flows in one direction (x) by the pressure gradient. Lubricants are incompressible Newtonian fluids, flows are laminates, and terminal effects are ignored. Find the maximum flow rate [m/s] when the pressure difference (△P/L) per unit length is 25000 Pa/m.Data: clearance between plates (B) = 6 mm, lubricant viscosity (μ) = 25 cP (1cP = 10-3 Pa·s), lubricant density (=) = 0.88 g/cm3 Please.. explain more easy
Taylor number (Ta) is used here to describe the ratio between the inertia effect andthe viscous effect. By applying Buckingham Pi’s Theorem, determine an equation forTa as a function of the radius of inner cylinder (r), cylinder tangential velocity (v),fluid dynamic viscosity (μ), gap distance (L) and fluid density (ρ).
As shown in Fig. 1.12, a horizontal interface 0-0 exists between two immiscible liquids. The dynamic viscosity of these two liquids are 0.14 Pa sand 0.24 Pa s respectively. The thickness is d1 0.8 mm and d2 1.2 mm respectively. Assuming that the velocity gradient is linear. Find theforce F required to push a bottom area A 1000 cm2 wood board to movewith velocity v0 0.4 m/s along the surface?
A dimensionless combination of variables that is important in the study of viscous flow through pipes is called the Reynolds number, Re, defined as ???/? where, as indicated in Fig. 11, ? is the fluid density, V the mean fluid velocity, D the pipe diameter, and the fluid viscosity. A Newtonian fluid having a viscosity of 0.38 ? . ?/?² and a specific gravity of 0.91 flows through a 25‐mmdiameter pipe with a velocity of 2.6 ?/?. Determine the value of the Reynolds number using (a) SI units, and (b) BG units.
Choose the correct answer Kinematic viscosity is * f. dynamic viscosity* Density b. About 1.2*10^-2 m2/s for water e. Both b and d c. Density*dynamic viscosity d. Both a and c g. Both f and c a. About 1.2*10^-6 m2/s for water
Air with density of 1.225 kg/m^3 and viscosity of 1.789 x 10^-5 kg/m-s flows in a wind tunnel, the wind tunnel spped is measured with Pitot tube probe. For a certain run, the stagantion pressure is measured to be 472.6 Pa gage and the statric pressure is 15.43 Pa gage. Calculate the wind tunnel speed. Choose the right answer below: a.16.3 m/s b.18. 3 m/s c.17. 3 m/s d.19. 3 m/s