Important variables in a particular water machine are: Fluid density (ρ), impeller angular velocity (ω), impeller diameter (D), volume flow rate (), fluid viscosity (µ), head (gH). In fact, (gH) shows the energy that the fluid unit mass receives from or gives to the machine, independent of gravitational acceleration (g). Therefore, gH value is used instead of H. Important sizes in terms of the operation of the water machine are power (P), (gH) and efficiency ( h). Derive dimensionless numbers by typing these two parameters based on the above variables and applying Buckingham's p method (repeating variables method).

Important variables in a particular water machine are: Fluid density (ρ), impeller angular velocity (ω), impeller diameter (D), volume flow rate (), fluid viscosity (µ), head (gH). In fact, (gH) shows the energy that the fluid unit mass receives from or gives to the machine, independent of gravitational acceleration (g). Therefore, gH value is used instead of H. Important sizes in terms of the operation of the water machine are power (P), (gH) and efficiency ( h). Derive dimensionless numbers by typing these two parameters based on the above variables and applying Buckingham's p method (repeating variables method).

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

Similar questions

The variables in a Saybolt viscometer are the time (t) required to empty a certain volume of oil of density (ρ) and viscosity (μ), a length (L) representing the dimensions of the viscometer, and the gravitational acceleration (g). Using the Buckingham Pi-theorem, show that
Resistance R to the motion of a completely submerged body is given by R = ρV2 L2 φ , where ρ and ν are density and kinematic viscosity of the fluid while L is the length of the body and V is the velocity of flow. If resistance of a one-sixth scale airship model when tested in water at 10 m/s is 230 N, what will be the resistance in air of the airship at the corresponding speed? Kinematic viscosity of air is 13 times that of water and density of water is 810 times of air.
Dimensional Analysis and Hydraulic Similitude (fluid mechanics) 1. Water at 60F at 12 ft/s in a 6-in. pipe. (a) For dynamic similarity, determine the velocity of medium fuel oil at 90F flowing in a 12-in. pipe. (b) Determine the diameter of the pipe that should be used if a medium lubricating oil at 70oF if flowing at a velocity of 50 ft/s. find the: a. velocity : ____________________ fps b. diameter : ____________________ in.
For most gases at standard or near standard conditions, the relationshipamong pressure, density, and temperature is given by the perfect gasequation of state: p = ρRT, where R is the specific gas constant. For airat near standard conditions, R = 287 J/(kg · K) in the International System of Units and R = 1716 ft · lb/(slug · ◦R) in the English Engineering System of Units. Using the above information, consider the following two cases: a. At a given point on the wing of a Boeing 727, the pressure andtemperature of the air are 1.9 × 104 N/m2 and 203 K, respectively.Calculate the density at this point.b. At a point in the test section of a supersonic wind tunnel, the pressureand density of the air are 1058 lb/ft2 and 1.23 × 10−3 slug/ft3,respectively. Calculate the temperature at this point.
When a person ice skates, the surface of the ice actuallymelts beneath the blades, so that he or she skates on a thinsheet of water between the blade and the ice.( a ) Find an expression for total friction force on the bottomof the blade as a function of skater velocity V , bladelength L , water thickness (between the blade and theice) h , water viscosity μ , and blade width W .( b ) Suppose an ice skater of total mass m is skatingalong at a constant speed of V 0 when she suddenlystands stiff with her skates pointed directly forward,allowing herself to coast to a stop. Neglecting frictiondue to air resistance, how far will she travelbefore she comes to a stop? (Remember, she iscoasting on two skate blades.) Give your answer forthe total distance traveled, x , as a function of V 0 , m ,L , h , μ , and W .( c ) Find x for the case where V 0 = 4.0 m/s, m = 100 kg,L = 30 cm, W = 5.0 mm, and h = 0.10 mm. Do youthink our assumption of negligible air resistance is agood one?
The absolute viscosity μ of a fluid is primarily afunction of( a ) Density, ( b ) Temperature, ( c ) Pressure, ( d ) Velocity,( e ) Surface tension
A fluid flows through a pipe and exits into a container that sits on some scales. At the beginning of the pipe the velocity is 6m/s After 156s, the scale shows 7733N. The pipe outlet diameter is 0.1m, and is four times greater than the inlet. Determine the density of a fluid
In medical work, pressures are often measured in units of mm of H2O because body fluids, including the cerebrospinal fluid, typically have nearly the same density as water. The pressure of the cerebrospinal fluid can be measured by means of a spinal tap. A hollow tube is inserted into the spinal column, and the height to which the fluid rises is observed. If the fluid rises to a height of 160 mm, we write its gauge pressure as 160 mm H2O. a) Sometimes it is necessary to determine whether an accident victim has suffered a crushed vertebra that is blocking the flow of cerebrospinal fluid in the spinal column. In other cases, a physician may suspect that a tumor or other growth is locking the spinal column and inhibiting the flow of cerebrospinal fluid. Such conditions can be investigated by means of the Queckensted test. In this procedure the veins in the patient’s neck are compressed, to make the blood pressure rise in the brain. The increase in pressure in the blood vessels is…
An important parameter in certain types of fluid flow problems when a free surface is present is the Froude number (Fr), which can be expressed in equation form as (Fr) = [pv^2/Lw]^1/2 where p is the density of the fluid, v is a velocity, L is a length, and w is the specific weight of the fluid. Show that the Froude number is dimensionless
A liquid is flowing at a volumetric flowrate of Q per unit width down a vertical surface. Obtain form dimensional analysis, the form of the relationship between Q and the film thickness. The flowrate Q is a function of density ρ, viscosity μ, film thickness δ and acceleration due to gravity g. Show that the volumetric flow rate is directly proportional to density if it is known that the flowrate is inversely proportional to the viscosity.
SAE 10W30 motor oil has a dynamic viscosity of 0.21 kilograms per meter second and a specific gravity of 0.896 (a) What is the density of the motor oil in units of kilograms per cubic meter?
The Ekman number, Ek, arises in geophysical fluiddynamics. It is a dimensionless parameter combining seawaterdensity ρ , a characteristic length L , seawaterviscosity μ , and the Coriolis frequency Ω sin φ , where Ωis the rotation rate of the earth and φ is the latitude angle.Determine the correct form of Ek if the viscosity is in thenumerator.