A liquid of density ? and viscosity ? is pumped at volume flow rate V· through a pump of diameter D. The blades of the pump rotate at angular velocity ? . The pump supplies a pressure rise ΔP to the liquid. Using dimensional analysis, generate a dimensionless relationship for ΔP as a function of the other parameters in the problem. Identify any established nondimensional parameters that appear in your result. Hint: For consistency (and whenever possible), it is wise to choose a length, a density, and a velocity (or angular velocity) as repeating variables.

A liquid of density ? and viscosity ? is pumped at volume flow rate V· through a pump of diameter D. The blades of the pump rotate at angular velocity ? . The pump supplies a pressure rise ΔP to the liquid. Using dimensional analysis, generate a dimensionless relationship for ΔP as a function of the other parameters in the problem. Identify any established nondimensional parameters that appear in your result. Hint: For consistency (and whenever possible), it is wise to choose a length, a density, and a velocity (or angular velocity) as repeating variables.

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 5.9P: When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the...

See similar textbooks

Similar questions

5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its bearing is found to be dependent on the force F normal to the shaft, the speed of rotation N of the shaft, the dynamic viscosity of the oil, and the shaft diameter D. Establish a correlation among these variables by using dimensional analysis.
When a capillary tube of small diameter D is inserted into a container of liquid, the liquid rises to height h inside the tube (Fig.). h is a function of liquid density ? , tube diameter D, gravitational constant g, contact angle ?, and the surface tension ?s of the liquid. (a) Generate a dimensionless relationship for h as a function of the given parameters. (b) Compare your result to the exact analytical equation for h. Are your dimensional analysis results consistent with the exact equation? Discuss.
A tiny aerosol particle of density ?p and characteristic diameter Dp falls in air of density ? and viscosity ?. If the particle is small enough, the creeping flow approximation is valid, and the terminal settling speed of the particle V depends only on Dp, ? , gravitational constant g, and the density difference (?p − ? ). Use dimensional analysis to generate a relationship for V as a function of the independent variables. Name any established dimensionless parameters that appear in your analysis.
Using primary dimensions, verify that the Rayleigh number is indeed dimensionless. What other established nondimensional parameter is formed by the ratio of Ra and Gr?
The time t d to drain a liquid from a hole in the bottom of atank is a function of the hole diameter d , the initial fluidvolume y 0 , the initial liquid depth h 0 , and the density ρ andviscosity μ of the fluid. Rewrite this relation as a dimensionlessfunction, using Ipsen’s method.
The thrust F of a propeller is generally thought to be afunction of its diameter D and angular velocity V , the forwardspeed V , and the density ρ and viscosity μ of the fl uid.Rewrite this relationship as a dimensionless function.
The output power W. of a spinning shaft is a function of torque T and angular velocity ? . Use dimensional analysis to express the relationship between W., T, and ? in dimensionless form. Compare your result to what you know from physics and discuss briefly
The pressure coefficient is defined by the ratio between the static pressure difference and the dynamic pressure (pictured): Where P is the static pressure [Pa], P∞ is the reference static pressure [Pa], ρ is the density [kg/m3], and V is the velocity [m/s]. Using the primary dimensions and their units, show that the pressure coefficient is dimensionless.
Dimensional analysis is to be used to correlate data on bubble size with the properties of the liquid when gas bubbles are formed by a gas issuing from a small orifice below the liquid surface. Assume that the significant variables are bubble diameter D, orifice diameter d, liquid density rho, surface tension sigma (in N/m), liquid viscosity mu, and g. Select d, rho, and g as the core variables.
A liquid of density ? and viscosity ? flows by gravity through a hole of diameter d in the bottom of a tank of diameter DFig. . At the start of the experiment, the liquid surface is at height h above the bottom of the tank, as sketched. The liquid exits the tank as a jet with average velocity V straight down as also sketched. Using dimensional analysis, generate a dimensionless relationship for V as a function of the other parameters in the problem. Identify any established nondimensional parameters that appear in your result. (Hint: There are three length scales in this problem. For consistency, choose h as your length scale.) except for a different dependent parameter, namely, the time required to empty the tank tempty. Generate a dimensionless relationship for tempty as a function of the following independent parameters: hole diameter d, tank diameter D, density ? , viscosity ? , initial liquid surface height h, and gravitational acceleration g.
During World War II, Sir Geoffrey Taylor, a British fl uiddynamicist, used dimensional analysis to estimate theenergy released by an atomic bomb explosion. He assumedthat the energy released E , was a function of blast waveradius R , air density ρ, and time t . Arrange these variablesinto a single dimensionless group, which we may term theblast wave number .
A prototype submarine moves at velocity V, in fresh water at 20 °C, at a 2-m depth, where ambient pressure is 128 kPa. Its critical cavitation number is known to be Ca = 0.25. At what velocity will cavitation bubbles begin to form on the body? Will the body cavitate if V = 30 m/s and the water is cold (5 °C)?