It is often said that electric current „flows“. Is this the only analogy between electric current and the flow of a liquid? Investigate theoretically and experimentally other analogies between these two things.

Condition of the problem:

0

zj

yj

xj zyx

Where j – current density (it equals to a charge, which is transferred through unit of cross-section in time unit).

movement of some quantity of substance in a space in time. :

0

zyxzyx

Value equals to liquid mass, which is transferred through unit of section in time unit.

The first Kirchgof's law (law of conservation of energy)

Electric current and a liquid flow.

Law of mass conservation:

–+

––

+

movement of charged particles (electrons or ions)

m q

Electric current and a liquid flow.

Ohm's law: xjx

yj

y

yjy

- electric potential,

- conductivity of given medium

Liquid movement.

tzyx ,,,

xx

yy

zz

Components of velocity:

Current.

02

2

2

2

2

2

zyx

02

2

2

2

2

2

zyx

Similarities:

• .Electric potential is analogous to potential of velocities .

• .Value corresponds to value .

• .Equipotential surfaces in electric current (x, y, z)=const are analogous to equipotential surfaces in liquid flow (x, y, z)=const.

j

Determinate conditions.

1. Liquid flow should be irrotational.

zv

yv yz

x 21 0

yzzy

2. Mentoined formulas model fluid nonviscous flow.

Newton’s formula:

n

where η - dynamic (absolute) coefficient

of velocity; - velocity gradient on normal to

ground, where stress acts;

vn

Movement of liquid in a tube.

ll

Re

Poiseuille’s equation (11):

421

128d

lppV

where p - pressure in the given point of a tube; V - discharge of liquid; l - length of the corresponding section of a

tube.

Reynolds number:

For laminar flow Re crRe<

Critical Reynolds number is 2300.

2212121

4d

lS

lRI

Corresponding express for the part of electric Corresponding express for the part of electric circuitcircuit::

p

Experimental setup

Pressure was determined by height of liquid lifting in a glass tube. Reynolds number calculated by experimental dates was not higher than some hundreds. From this follows, that we can consider flow as laminar.

0 100 200 300 400 500 600 700

05

1015202530354045505560657075808590

H, m

m.

L, mm.

0,04 0,05 0,06 0,07 0,08 0,09 0,10 0,11 0,12

0,02

0,04

0,06

0,08

0,10

0,12

0,14

dp/d

l, re

l. un

.

dm/dt, rel. un.

Dependence of height of liquid column in glass tube

on lenght of conductor L for different liquid velocities.

Dependence of ratio on

discharge of liquid

dpdl

Tubes with different diameters and lengths.

Mariotte’s vessel. This setup is guaranteed constant pressure difference and, therefore, constant discharge in the process of experiment.

"Subcurcuit"Tube №1Tube №2Series connectionParallel connection

"Resistance"

Experimental setupExperimental setup

160420590125

0,0 0,1 0,2 0,3 0,4 0,5

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

experiment theory

Dis

char

ge o

f wat

er (k

g/m

in)

Pressure difference (atm)

The dependence of discharge on pressure difference in the ends of one conductor.

Dependence of resistance on

number parallel tubes.

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,60

10

20

30

40

50

experiment theory

"Res

ista

nce"

(m2 s-1

kg-1)

Length of pipe (m)

1 2 3 40

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

theory experiment

"Res

ista

nce"

(m2 s-1

kg-1)

Number of equal resistors

Dependence of resistance on length of tubes (series connection).

Bridge circuit

• Condition of current absence in a conductor R5:

4

3

2

1

RR

RR

Experimental setup.Experimental setup.Liquid in connection element does not move, when lengths

of corresponding tubes are proportional or equal.

Alternate currentAnalogues to an induction coil and a condenser.

Condenser properties:• It doesn’t let current pass, but collects

charge on its plates until breakdown.• Creates electrostatic field between plates.• Charged condenser has energy.

Induction coil properties:• Coil prevents from sharp change of electric current.• It also has energy if electric current flows through it.

Field transistor

• This element, depending on potential of bibb, conduct or not electrical current.

In the point A constant head pressure is created. Depending on the pressure in the point B plunger let or not pass water.

Oscillatory circuit.

• “Transistor” plays a role of feed-back. Current in the induction coil corresponds to the liquid movement in section CD. Energy of charged condenser is replaced by potential energy of liquid.

Logical elements:Element Element ““AndAnd””.. Element Element ““OrOr””.. ““XorXor”” element element..

Only in the presence of overpressure in each of cross-sections 1, 2 liquid flow is taken place.

Liquid will move from point A to point B in the presence overpressure in one or in both of the cross-sections 1, 2.

Liquid moves from point A to B in the presence overpressure only in one of cross-sections 1, 2, not in both.

In fact the flow of a liquid and electric current are different. They are different in

their physical meaning at first. But if try we can find out some similarities which appe-

ars after some analogues were made.