* The volume of liquid flowing per second is called the volume flow rate Q and has the dimensions of [L][T]. The flow rate of a liquid through a hypodermic needle during an injection can be estimated 60. with the following equation: TR"(P, – P,) 8nL The length and radius of the needle are L and R, respectively, both of which have the dimension [L]. The pressures at opposite ends of the nee- dle are P, and P, both of which have the dimensions of [M]/{[L][T]*}. The symbol 7 represents the viscosity of the liquid and has the dimen- sions of [M]/{[L][T]}. The symbol 7 stands for pi and, like the number 8 and the exponent n, has no dimensions. Using dimensional analysis, de- termine the value of n in the expression for Q.

* The volume of liquid flowing per second is called the volume flow rate Q and has the dimensions of [L][T]. The flow rate of a liquid through a hypodermic needle during an injection can be estimated 60. with the following equation: TR"(P, – P,) 8nL The length and radius of the needle are L and R, respectively, both of which have the dimension [L]. The pressures at opposite ends of the nee- dle are P, and P, both of which have the dimensions of [M]/{[L][T]*}. The symbol 7 represents the viscosity of the liquid and has the dimen- sions of [M]/{[L][T]}. The symbol 7 stands for pi and, like the number 8 and the exponent n, has no dimensions. Using dimensional analysis, de- termine the value of n in the expression for Q.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

1. Dimensional Analysis of Fluid Flow in a Pipe Consider fluid flow in a long cylindrical pipe of diameter D. A fluid with viscosity i and density p flows through the pipe with an average velocity of V. The internal surface of the pipe is rough, with the average height of the roughness being h. We wish to determine how the pressure gradient dp/dz depends on the properties of the system through dimensionless groups. (a) Identify the relevant parameters and their dimensions. (b) Determine the number of relevant non-dimensional groups. (c) Select the dimensionally-independent scaling variables. (d) Determine the dimensionless group that relates dp/dz to the other relevant dimen- sionless groups.
An object hangs from a spring balance.The balance registers 32 N in air, 22 N when this object is immersed in water, and 27 N when the object is immersed in another liquid of unknown density. What is the density of that other liquid? Number i Units V
▾ Part A What gauge pressure must a pump produce to pump water from the bottom of the Grand Canyon (elevation 730 m) to Indian Gardens (elevation 1370 m)? Express your result in pascals and in atmospheres. Pgauge 6.27x108 Pa Submit ✓ Correct Part B Pgauge= Previous Answers Submit VΓΙΑΣΦ Request Answer ? atm
1. If in a given problem, there are N variables and M dimensions, how many repeating variables should be chosen? 2. The lift force FL on a wing is dependent on six (6) parameters: the fluid speed V, the chord length Lc, the fluid density p, the fluid viscosity , the speed of sound c in the fluid, and the angle of attack a of the wing. How many dimensionless products or tt-groups can be formed? 3. The lift force FL on a wing is dependent on six (6) parameters: the fluid speed V, the chord length Lc, the fluid density p, the fluid viscosity µ, the speed of sound c in the fluid, and the angle of attack a of the wing. Which of the following sets of variables are most appropriate to be chosen as the repeating variables? a. V, Lo, and p b. FL, V, and p c. V and p only d. V, c, and L. 4. The pipe wall shear stress Tw is dependent on the average velocity on the pipe V, the fluid density p, the fluid viscosity µ, the pipe diameter D, and roughness height ɛ along the wall of the pipe. Which of…
which of the two mass should i use to get density?
Question 1 a) A container of volume 2000 cm3 is completely filled by carefully pouring 1.7 kg of powder into it. The powder has a Carr’s Index of 25% and particle density of 1.40 kgm3. What is the bulk density of the powder? B)Calculate the bulk density of the powder in the container in part a) if it is tapped repeatedly. C) Calculate the voidage of the powder before and after tapping
Column A (a) Volume of a liquid (b) Area of a leaf (c) S.I. unit of volume (d) S.I. unit of density (e) S.I. unit of speed Column B (i) kg m-³ (ii) m³ (iii) graph paper (iv) m s-1 (v) measuring cylinder
(1) a. Gold is sold by the troy ounce (31.103 g). What is the volume (in cm3) of 2 troy ounces of pure gold? cm3 b. Mercury is commonly supplied in flasks containing 34.5 kg (about 76 Ib). What is the volume in liters of this much mercury? C. A straightforward method of finding the density of an object is to measure its mass and then measure its volume by submerging it in a graduated cylinder. What is the density (in g/cm?) of a 200 g rock that displaces 81.0 cm³ of water? (Note that the accuracy and practical applications of this technique are more limited than a variety of others that are based on Archimedes' principle.) g/cm3
Gg
ICE ANOTHER Alloys of gold are rated in karats, a dimensionless unit that is used to indicate the proportion of gold by weight in a gold-containing alloy. If an alloy is one part in twenty-four pure gold, then it is classified as one karat gold. The density of gold is 19.3 × 103 kg/m3. Determine the volume of gold in a 23.0 karat gold necklace that has a weight of 1.63 N. m3 Additional Materials O Reading
Liquid pressure The pressure P acting at a point in a liquid is directly proportional to the distance d from the surface of the liquid to the point. (a) Express P as a function of d by means of a formula that involves a constant of proportionality k. (b) In a certain oil tank, the pressure at a depth of 2 feet is 118 Ib/ft. Find the value of k in part (a).
Use dimension analysis to determine the drag force, F, on a sphere moving through a fluid, in terms of the radius of the sphere, r, the velocity of the sphere, v and the viscosity of the fluid, µ. A. F = krv¬1µ¯1 B. F = kr-1v-1µ C. F = krvµ D. F = krv-'µ %3D