§1.5 Forces acting on the fluid

When analyzing the forces applied on the fluid, an isolated body taken from the fluid is a part of fluid surrounded by any closed surface.The forces acting on the isolated body of the fluid can be categorized into surface force and mass force.

1.5.1 Surface force

Surface force is contact force which adj acent fluid or other obj ects directly exert on the surface of isolated body of fluid.In other words, Surface force denoted Fsis the force that acts across an internal or external surface element in a material body.The magnitude of surface force is proportional to cross sectional area of the moving fluid. Surface force can be decomposed into two perpendicular components:pressure and stress forces.Pressure force acts normally over an area and stress force acts tangentially over an area.The isolated body is taken as the research obj ect in the moving fluid as shown in Fig.1-7 and an area element ΔA was taken at the point A on the surface of the isolated body.Then pressure force is

where ΔFp is the pressure acting on the area element ΔA.

And stress force is

where ΔFτ is the stress force acting on the area element ΔA.

The SI unit of both pressure and stress forces is Pa (N/m2).

1.5.2 Mass force

Mass force is a force which acts on each fluid particle in the isolated body.Mass force is proportional to mass.

Unit mass force is the mass force acting on unit mass fluid:

where fx, fy and fz are mass forces which act on unit mass fluid in the direction of x, y and z coordinate, respectively.The unit of unit mass force is the same as that of acceleration.The most common mass force is gravity and inertia force.

For a static flow under gravity, if z axis is perpendicular to the upper, the component of unit mass force of fluid in each direction is:

fx=fy=0, fz=-g

Questions

1.1 What's continuum model of fluid? Continuum model is suitable for the liquid with bubbles?

1.2 Why is water regarded as incompressible fluid?

1.3 What's the most important characteristic of fluids different from solids?

1.4 What factors are related to fluid viscosity? How fluid viscosity varies with temperature?

1.5 The relationship curve betweenτof Newtonian fluid and has a fixed slope. If the slope of the relationship curve betweenτof a fluid and is fixed, must this fluid Newtonian fluid?

1.6 Which one is Newtonian fluid among the fluids below:

A.Inviscid fluid; B.Completely incompressible fluid;

C.Inviscid and incompressible fluid

1.7 Do ideal fluids have energy loss or not? Why?

1.8 How much is unit mass force which acts on the fluid in free fall?

Exercises

1．If the density of kerosene is 808 kg/m3, how much is the mass and weight of the kerosene with the volume of 2×10-3m3?

2．If pistol was pressurized, the volume of the liquid in the cylinder block is 10-3m3 when the pressure is 0.1 MPa and the volume is 9.94×10-4m3when the pressure is 10 MPa.Calculate the bulk modulus.

3．As shown in the Fig.1-8, the distance between the two horizontal plates is 0.5 mm and liquid was trapped between the two horizontal plates.The upper plate moves at the velocity of 0.25 m/s in the horizontal direction and the pressure is 2 Pa. Calculate the viscosity of liquid.

4．Calculate the fluid viscosity between the shaft and the shaft sleeve (see the Fig.1-9).