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friction and viscosity are negligibly small.
with water. An orifice of area s < S is opened in vessel. Neglecting the viscosity of wa- ter, determine how soon all the water will pour out of the vessel. 1.324. A horizontally oriented tube
the bottom of the
1.1!
h
angular velocity co about a stationary
Find the velocity of the fluid relative to the tube as a function of the column
v _
1.325. Demonstrate that in the case of a steady flow of an ideal fluid Eq. Fig. 1.83. (1.7a) turns into Bernoulli equation. 1.326. On the opposite sides of a wide vertical vessel filled with water two identical holes are opened, each having the cross-sectional
Fig. 1.84. Fig. 1.85.
Ah = 51 cm. Find the resultant force of reaction of the water flow- ing out of the vessel. 1.327. The side wall of a wide vertical cylindrical vessel of height
water. Find the resultant force of reaction of the water flowing out of the vessel immediately after the slit is opened. 1.328. Water flows out of a big tank along a tube bent at right an-
of reaction forces of flowing water, acting on the tube's walls, relative
64
C Z
Fig. 1.87.
Fig. 1.89.
Fig. 1.86.
Fig. 1.88.
Po.
in a cylindrical cavity filled with oil whose viscosity it (^) = 0.08 P
5-9451 (^65)
viscosities of glycerin and water are equal to rh = 13.9 P and 12 = = 0.011 P respectively. 1.338. A lead sphere is steadily sinking in glycerin whose viscosity is equal toil = 13.9 P. What is the maximum diameter of the sphere at which the flow around that sphere still remains laminar? It is known that the transition to the turbulent flow corresponds to Rey- nolds number Re = 0.5. (Here the characteristic length is taken to be the sphere diameter.) 1.339. A steel ball of diameter d = 3.0 mm starts sinking with zero initial velocity in olive oil whose viscosity is 1 = 0.90 P. How soon after the beginning of motion will the velocity of the ball differ from the steady-state velocity by n = 1.0%?
1.8. RELATIVISTIC MECHANICS
1 โ (v/c) where /0is the proper length and Atois the proper time of the moving clock.
โ XVIC 2 โ (^) e โ (V/c)2 โ^ (V/c)2^ โข^
(1.8b)
where t12is the time interval between events 1 and 2, /12is the distance between the points at which these events occurred.
(1.8e)
(1.8f)
(1.8g)
' vsโ^ V^ vy"1/-1 โ^ (V/c) voc 1 โvxV/c2 '
v, 1 โvxV/c
M โ mo^ p= my^ = MoV y1โ (v/02^ y^ 1โ (v/ where mois the rest mass, or, simply, the mass.
/ = /0 -V 1 โ(v/c)2 , At= A to^ (1.8a)
5* 67
where E and p are the total energy and momentum of the system prior to the collision, and mois the rest mass of the particle (or the system) formed.