1.311. What work has to be performed to make a hoop out of a
steel band of length 1 = 2.0 m, width h = 6.0 cm, and thickness
6 = 2.0 mm? The process is assumed to proceed within the elasticity
range of the material.
1.312. Find the elastic deformation energy of a steel rod whose
one end is fixed and the other is twisted through an angle cp = 6.0°.
The length of the rod is equal to 1 = 1.0 m, and the radius to r =
= 10 mm.
1.313. Find how the volume density of the elastic deformation
energy is distributed in a steel rod depending on the distance r from
its axis. The length of the rod is equal to 1, the torsion angle to (p.
1.314. Find the volume density of the elastic deformation energy
in fresh water at the depth of h = 1000 m.1.7. Hydrodynamics
- The fundamental equation of hydrodynamics of ideal fluid (Eulerian
equation):
dv
P dt f —V P'
where p is the fluid density, f is the volume density of mass forces (f = pg i n
the case of gravity), Vp is the pressure gradient. - Bernoulli's equation. In the steady flow of an ideal fluid
pv 2
2 - Fpgh+p= const^ (1.7b)
along any streamline. - Reynolds number defining the flow pattern of a viscous fluid:
Re = p (1.7c)
where 1 is a characteristic length, 11 is the fluid viscosity. - Poiseuille's law. The volume of liquid flowing through a circular tube
(in m 3 /s):
70 4 Pi- Pa
Q — 811 / ' (1.7d)
where R and 1 are the tube's radius and length, pi — p^2 is the pressure differ-
ence between the ends of the tube.- Stokes' law. The friction force on the sphere of radius r moving through
a viscous fluid:
F (1.7e)
1.315. Ideal fluid flows along a flat tube of constant cross-section,
located in a horizontal plane and bent as shown in Fig. 1.80 (top
view). The flow is steady. Are the pressures and velocities of the fluid
equal at points / and 2? What is the shape of the streamlines?
1.316. Two manometric tubes are mounted on a horizontal pipe
of varying cross-section at the sections Si and 82 (Fig. 1.81). Find
(1.7a)