Explanation Write the expression for the depth of the plate. h = f ( d , g , μ , V , ρ ) (I) Here, the distance is d , the depth of the plate is h , the volume of poured fluid is V , the density of the fluid is ρ , the viscosity of the fluid is μ , and the acceleration due to gravity is g . Write the dimension of the distance in F L T unit system. d = [ L ] (II) Here, the dimensions for distance is L . Write the dimension of the volume of poured fluid in F L T unit system. V = [ L 3 ] (III) Here, the dimensions for volume of poured fluid is L 3 . Write the dimension of the gravitational acceleration in F L T unit system. g = [ L T − 2 ] (IV) Here, the dimension for distance is L and the time is T . Write the expression for density. ρ = m v (V) Here, the mass is m , the volume is v and the density is ρ . Substitute [ F L − 1 T 2 ] for m and [ L 3 ] for v in Equation (IV). ρ = [ F L − 1 T 2 ] [ L 3 ] = [ F L − 4 T 2 ] (VI) Here, the dimensions for force is F and the dimension for diameter is L . Write the expression for absolute viscosity. μ = u ρ (VII) Here, the kinematic viscosity is u and the density of the fluid is ρ . Substitute [ L 2 T − 1 ] for u and [ F L − 4 T 2 ] for ρ in Equation (VII). μ = [ L 2 T − 1 ] × [ F L − 4 T 2 ] = [ F L − 2 T ] (VIII) Here, the dimension for force is F , the dimensions for length is L and the dimension for time is T . Write the dimension of the depth in F L T unit system. h = [ L ] (IX) Here, the dimensions for depth is L . Write the expression for the number of variable. n = k − r (X) Here, the number of variable is k , the number of dimensions is r and the number of pi terms is n . Write the expression for first pi terms. Π 1 = t d a g b ρ c (XI) Here, the constant are a , c and b . Write the dimension for pi term. Π = L 0 T 0 (XII) Write the expression for second pi terms. Π 2 = V d a g b ρ c (XIII) Write the expression for third pi terms. Π 3 = μ d a g b ρ c (XIV) Write the expression for pi terms. Π 1 = f ( Π 2 , Π 3 ) (XV) Write the dimension of the time in F L T unit system. t = [ T ] (XVI) Here, the dimensions for time is T . Conclusion: The number of variable is 6 and the number of dimensions is 3 . Substitute 6 for k and 3 for r in Equation (XIII). n = 6 − 3 = 3 Substitute [ L ] for d , [ F 0 L 0 T 0 ] for Π 1 , [ L T − 2 ] for g , [ T ] for t and [ F L − 4 T 2 ] for ρ in Equation (XI). [ F 0 L 0 T 0 ] = [ T ] [ L ] a [ L T − 2 ] b [ F L − 4 T 2 ] c [ F 0 L 0 T 0 ] = [ T ] [ L a ] [ L b T − 2 b ] [ F c L − 4 c T 2 c ] [ F 0 L 0 T 0 ] = [ F c L a + b − 4 c T − 2 b + 1 + 2 c ] (XVII) Compare the exponents of F in Equation (XVII). c = 0 (XVIII) Compare the exponents of T in Equation (XVII). − 2 b + 1 + 2 c = 0 2 b = 1 + 2 c b = 1 + 2 c 2 (XIX) Compare the exponents of L in Equation (XVII). a + b − 4 c = 0 a = 4 c − b (XX) Substitute 0 for c in Equation (XIX). b = 1 + 2 ( 0 ) 2 = 1 2 (XXI) Substitute 1 2 for b and 0 for c in Equation (XX). a = 4 ( 0 ) − 1 2 = − 1 2 (XXII) Substitute 0 for c , − 1 for b and − 1 2 for a in Equation (XI). Π 1 = t d − 1 2 g 1 2 ρ 0 = t g 1 / 2 d 1 / 2 = t g d (XXIII) Substitute [ L ] for d , [ L T − 2 ] for g and [ T ] for t in Equation (XXIII)

8th Edition

ISBN: 9781119547990

Author: HOCHSTEIN

Publisher: JOHN WILEY+SONS INC.

See similar textbooks

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 condit…

Videos

Question

Chapter 7.5, Problem 27P

To determine

The set of dimensional parameters.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.3, Problem 26P

Chapter 7.5, Problem 28P

Students have asked these similar questions

Consider a regenerative gas turbine power plant with two stages of compression and two stages of expansion. The compressor pressure ratio of the compressor is 3. Air enters each stage of compressor at 290 K and each stage of turbine at 1400 K. The regenerator has an effectiveness of 100%. Determine (a) The enthalpy at stage#2 in KJ/kg⭑ (b) The enthalpy at stage#6 in KJ/kg* (c) The enthalpy at stage#9 in KJ/kg (d) The enthalpy at stage#10 in KJ/kg (e)The mass flow rate of air needed to develop a net power output of 50 MW* *For all final answers please enter the integer part only, (ie 1234) and do not include the decimal part and the decimal point No rounding in your calculation. Compressor stage 1 Regenerator www HX ww 9 Combustor Reheat Intercooler ww Compressor stage 2 Turbine 1 combustor Turbine 2

Design a proportional derivitivecontroller for a plant orsystemthat satisfies the following specifications : 1. is steady-state error is less than 2 % for a ramp input. 2.) Damping ratio (zeta) is greater than 0.7have determined the 3. Once youvalue of kp and kd, then plotthe response of the compensated(with controller) and uncompensated( without the controller, only the plantsystem using MATLAB.

Example 2 The particle has a mass of 0.5 kg and is confined to move along the smooth horizontal slot due to the rotation of the arm OA. Determine the force of the rod on the particle and the normal force of the slot on the particle when 0 = 30°. The rod is rotating with a constant angular velocity 2 rad/s. Assume the particle contacts only one side of the slot at any instant. B =2 rad/s 0.5 m 0.5(9.81)N r F 30° N

Chapter 7 Solutions

EBK MUNSON, YOUNG AND OKIISHI'S FUNDAME

Ch. 7.1 - Prob. 1P Ch. 7.1 - An equation used to evaluate vacuum filtration...Ch. 7.1 - Verify the left-hand side of Eq. 7.2 is...Ch. 7.1 - The Reynolds number, ρVD/μ, is a very important...Ch. 7.1 - For the flow of a thin film of a liquid with a...Ch. 7.1 - Prob. 6P Ch. 7.3 - A mixing basin in a sewage filtration plant is...Ch. 7.3 - The excess pressure inside a bubble (discussed in...Ch. 7.3 - At a sudden contraction in a pipe the diameter...Ch. 7.3 - Water sloshes back and forth in a tank as shown in...

Ch. 7.3 - Assume that the flowrate, Q, of a gas from a...Ch. 7.3 - The pressure rise, Δp, across a pump can be...Ch. 7.3 - Prob. 13P Ch. 7.3 - Prob. 14P Ch. 7.3 - Prob. 15P Ch. 7.3 - A cone and plate viscometer consists of a cone...Ch. 7.3 - Prob. 17P Ch. 7.3 - A cylinder with a diameter D floats upright in a...Ch. 7.3 - Prob. 19P Ch. 7.3 - Prob. 20P Ch. 7.3 - Experiments are conducted on a washing machine...Ch. 7.3 - Prob. 22P Ch. 7.3 - Prob. 23P Ch. 7.3 - Prob. 24P Ch. 7.3 - Prob. 25P Ch. 7.3 - Prob. 26P Ch. 7.5 - Prob. 27P Ch. 7.5 - Prob. 28P Ch. 7.5 - Prob. 30P Ch. 7.5 - A screw propeller has the following relevant...Ch. 7.6 - Shown in the following table are several flow...Ch. 7.6 - A large, hot plate hangs vertically in a room....Ch. 7.6 - Develop the Weber number by starting with...Ch. 7.6 - Develop the Froude number by starting with...Ch. 7.6 - The following dimensionless groups are often used...Ch. 7.6 - Prob. 37P Ch. 7.7 - Prob. 38P Ch. 7.7 - The pressure drop, Δp, over a certain length of...Ch. 7.7 - Prob. 40P Ch. 7.7 - In order to maintain uniform flight, smaller birds...Ch. 7.7 - A 250-m-long ship has a wetted area of 8000 m2. A ...Ch. 7.7 - Prob. 45P Ch. 7.8 - Air at 80 °F is to flow through a 2-ft pipe at an...Ch. 7.8 - A model of a submarine, 1:15 scale, is to be...Ch. 7.8 - The drag characteristics of a torpedo are to be...Ch. 7.8 - For a certain fluid flow problem it is known that...Ch. 7.8 - The fluid dynamic characteristics of an airplane...Ch. 7.8 - If an airplane travels at a speed of 1120 km/hr at...Ch. 7.8 - (See The Wide World of Fluids article “Modeling...Ch. 7.8 - Prob. 54P Ch. 7.8 - Prob. 55P Ch. 7.8 - Prob. 56P Ch. 7.8 - Prob. 57P Ch. 7.8 - Prob. 58P Ch. 7.8 - Prob. 59P Ch. 7.8 - Prob. 60P Ch. 7.8 - Prob. 61P Ch. 7.8 - Prob. 62P Ch. 7.8 - As shown in Fig. P7.63, a “noisemaker” B is towed...Ch. 7.8 - The drag characteristics for a newly designed...Ch. 7.8 - The drag characteristics of an airplane are to be...Ch. 7.8 - The drag on a sphere moving in a fluid is known to...Ch. 7.8 - A dam spillway is 40 ft long and has fluid...Ch. 7.8 - Prob. 68P Ch. 7.8 - Prob. 69P Ch. 7.8 - Prob. 70P Ch. 7.8 - Prob. 71P Ch. 7.9 - Prob. 72P Ch. 7.9 - At a large fish hatchery the fish are reared in...Ch. 7.9 - Prob. 75P Ch. 7.9 - Prob. 76P Ch. 7.9 - Prob. 77P Ch. 7.9 - Prob. 78P Ch. 7.9 - Prob. 79P Ch. 7.9 - Prob. 80P Ch. 7.9 - Prob. 81P Ch. 7.9 - Prob. 82P Ch. 7.10 - Prob. 83P Ch. 7.10 - Prob. 84P Ch. 7.10 - Prob. 85P Ch. 7.10 - Prob. 86P Ch. 7.10 - Prob. 87P Ch. 7.10 - Prob. 88P Ch. 7.11 - Prob. 1LLP Ch. 7.11 - Prob. 2LLP

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.