The resistance to motion R for a sphere of diameter d moving at constant velocity u through a compressible fluid is dependent on the density p and the bulk modulus K. The resistance is primarily due to the compression of the fluid in front of the sphere. Show that the dimensionless relationship between these quantities is given by: Ne=(Ma)

The resistance to motion R for a sphere of diameter d moving at constant velocity u through a compressible fluid is dependent on the density p and the bulk modulus K. The resistance is primarily due to the compression of the fluid in front of the sphere. Show that the dimensionless relationship between these quantities is given by: Ne=(Ma)

Name: 1. The resistance to motion R for a sphere of diameter d moving at con
Uploaded: 2024-03-20T06:56:55.000Z
Channel: Bartleby
Description: 1. The resistance to motion R for a sphere of diameter d moving at constant velocity u through a compressible fluid is dependent on the density p and the bulk modulus K. The resistance is primarily due to the compression of the fluid in front of the

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter1: Introduction To Statics

Section: Chapter Questions

Problem 1.13P: Determine the dimensions of constants A and B far which the following equation is dimensionally...

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.
Determine the dimensions of constants A and B far which the following equation is dimensionally homogeneous: F=Akx2sinBxk where F is a force, x is a distance, and k represents stiffness (dimensions: [FL1]).
Prove that the pressure at a point is equal in all directions for a fluid at rest with respect to thestationary Cartesian coordinate system XYZ. Comparatively analyse also the definitions of stress andpressure
1. The height of the manometer depends on the _______ of the manometric fluid.2. _______ gives the interaction between the pressure acting at a point on the surface of the liquidand velocity of its particle. It states that the total energy of a small amount of an incompressibleliquid flowing from one point to another remains constant throughout the displacement.3. _______ states that the buoyant force or up thrust experience by an object immersed in a liquidis equal to the weight of the liquid displaced.4. The upward force experienced by a body when partially or wholly immersed in a fluid iscalled _______.5. _______ states that the velocity of the fluid through an orifice is equal to that which a body wouldattain in falling freely from the free surface of the liquid to the orifice.6. A floating body is known to be _______ when the metacentric height is above the center ofgravity.
A spherical neutrophil 16µm in diameter is resting as shown in the attached photo. The pressure difference between the inside and outside of the cell is 7.5Pa. a) Draw free body diagrams of the whole cell and one hemisphere of the cell. b) Calculate cortical tension in the cell. In a micropipette aspiration experiment, a suction pressure of 52.5 Pa was used to aspirate the neutrophil membrane. c) Draw free body diagrams of the whole cell under micropipette aspiration and the portion of the cell in the micropipette. What is the diameter of the micropipette tip used to make this hemispherical projection? Next, the micropipette aspiration was stopped, and the cell was treated with Cytochalasin D, an inhibitor of actin polymerization, causing the cortical tension to decrease by half. d) Assuming the pressures inside and outside the cell have not changed, what is the new cell radius? e) If the same micropipette was used to aspirate the cell, what would be the new suction pressure?
C1 (a). A lubricating oil having the dynamic viscosity of 0.055 poise and kinematic viscosity of 0.17 stokes. Calculate (i) the density of oil in kg/m3, (ii) the weight density of oil in N/m3,(iii) the specific gravity, and (iv) the specific volume in m3/kg. C1 (b). Calculate the capillary effect in mm in a glass tube of 4.4 mm diameter, when immersed in (1) water (2) mercury. The values of surface tension in contact with air are 0.0737 N/m and 0.54 N/m respectively. The contact angle for water =00 and mercury =1300. (Enter only the values by referring to the unit given. Also, upload the handwritten answers in the link provided) C1(a).(i).The density of oil in kg/m3 C1(a). (ii) the weight density of oil in N/m3 C1(a). (iii) the specific gravity C1(a). (iv) the specific volume in m3/kg C1 (b). 1.The capillary effect (water) in mm C1 (b). 2.The capillary effect (mercury) in mm
In rotating a thin circular disc submerged in a fluid, a torque has to be applied to the disc to overcome the frictional resistance of the fluid. Using dimensional analysis, show that where T is the applied torque and D is the diameter of a disc rotating at a speed N in fluid of viscosity u and density p.
2.) We are on the space station, so there is no effective gravity. In a small fluid experiment, a small spherical bacteria of 1 mm radius is moving at a speed of +1.50 mm/second horizontally in the fluid. The bacteria has a density of 1500. kg/m^3. (3a) Draw a free-body diagram, labeling all forces and show the likely direction of Fnet (3b) What is the mass of the bacteria? (3c) If the value of the viscosity is 1.25 kg/m/s, then what is the net acceleration experienced by the bacteria at that moment.
1. A special-purpose piece of laboratory glassware, called a pyncnometer; is used to measureLiquid densities. It has a volume of 25 cc, and a mass of 17 .24 g when it is full of air. Whenfilled with a liquid of unknown density, its mass = 45.00 g. What is the density of this liquid?How large an error do we make if we ignore the mass of the air that was in it when we weighed itand found m = 17.24 g?
When a liquid of volume 4 liter is subjected to an additional pressure of 5 x 107 N/m2, the change in the volume is found to be 4 ml, calculate the Bulk modulus of the liquid
The volume and the average density of an irregularly shaped body are to be determined by using a spring scale. The body weighs 7000 N in air and 4700 N in water. Determine the volume and the density of the body. State your assumptions.
Determine the density of a fluid having viscosity 0.04 poise and kinematic viscosity 0.044 stokes The density of the liquid in kg/m3 Answer