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EXPERIMENT 1
AIM : To verify Bernoullis Theorem and plot graph between
(a) Pressure Head v/s the length of pipe(b) Kinematic head v/s
Length
(c) Total Head v/s Length
INTRODUCTION :
Theorem is one of the most important equations in fluid
mechanics. The
theorem is based on the law of conservation of energy. According
to
Bernoullis Theorem, in an ideal, incompressible, steady and
The
Bernoullis continuous flow, the sum of the pressure energy,
potential
energy, and the kinetic energy per unit weight of the fluid is
constant.
The energy per unit weight of the fluid (Nm/N) has got the
dimensions of
length (L) and can be expressed in metres of the fluid column,
commonly
called head. Thus according to Bernoullis Theorem, the sum of
the
pressure head (p/), datum head (Z), and the velocity head
(V2/2g) is
constant, i.e. p/ + Z + V2/2g = constant.
In case of real fluids, because some energy is always lost in
overcoming
frictional resistance, the Bernoulli theorem for real fluids
is
p1/ + V12/2g + Z1 = p2/ + V2
2/2g + Z2 + HL
where HL is the loss of head from sections 1 to 2.
EXPERIMENTAL SET-UP :
The set-up consists of a horizontal converging-diverging duct
having a
constant width but varying depth. The duct is made of
transparent Perspexsheets. A number of piezometers are fitted on
the duct to indicate the
piezometric levels of varying sections. (see figure)
The duct is connected to a constant-head supply tank at one end.
The supply
tank is fitted with a piezometer to indicate the water depth.
The overflow
pipe in the tank discharges the excess water and thus keeps the
water level
constant.
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The water is collected in a measuring tank for the determination
of the
discharge.
A small tank with a valve is provided at the downstream of the
duct.
A graph paper can be fixed on a wooden board fixed behind the
piezometric
tubes for marking the water levels.
THEORY :
According to Bernoullis theorem,
p1/ + V12/2g + Z1 = p2/ + V2
2/2g + Z2
The pressure head is indicated by the piezometers at various
sections. For
the horizontal duct, if the datum is taken as the axis of the
duct, the datum
head is zero. The velocity head can be calculated from the
discharge Q.
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V12/2g = (Q/A1)
2 / 2g
V22/2g = (Q/A2)
2 / 2g
where A1 and A2 are the areas of cross-sections at two sections
1 and 2
respectively.The discharge is calculated from the volume of
water (V) collected in time t.
Q = V/t
The loss of head at various sections can be calculated from the
equation
p1/ + V12/2g + Z1 = p2/ + V2
2/2g + Z2 + HL1 = p3/ + V32/2g
+ Z3 + HL2 etc.
PROCEDURE :
1. Measure the heights of the duct at various sections using a
scale. Also
measure the distances of various sections from the inlet of the
duct.
2. Gradually open the outlet valve. The water level rises in
various
piezometers. When the flow becomes steady, measure the heights
of
water columns at various sections.
3. Measure the water depth in the constant-head supply tank,
as
indicated by its piezometer.4. Take the initial reading of the
water level in the measuring tank and
start the stop-watch.
5. Note the final water level after a suitable time period.
6. Repeat steps (2) to (5) after increasing the discharge by
using the
outlet valve.
Take 2 sets of observations.
OBSERVATIONS AND CALCULATIONS :
Width of the duct b = cm
Length of the collecting (measuring) tank L = cm
Width of the collecting (measuring) tank B = cm
Area of cross-section of the tank A = L B = m2
I SET Constant head H0 = cm
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Discharge measurement :
Initial level, y1 = cm
Final level, y2 = cm
Rise, y = cm
Volume = y A = m3
Time, t = seconds
Discharge, Q = volume/time = m3/s
Let w(weight density) = g
S.No. Area10-3
(m2)PressureHead
(P/w)
(cm)
Velocityin cm/s
VelocityHead (cm)
V2/2g
Totalhead
(P/w)+
V2/2g
(in cm)
1.
2.
3.
4.
5.6.
7.
8.
9.
10.
11.
I I SET
Constant head H0 = cm
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Discharge measurement :
Initial level, y1 = cm
Final level, y2 = cm
Rise, y = cm
Volume = y A = m3
Time, t = seconds
Discharge, Q = volume/time = m3/s
Let w(weight density) = g
S.No. Area10-3
(m2)
Pressure
Head
(P/w)
(cm)
Velocity
(in cm/s)
Velocity
Head (cm)
V2/2g
Total
head
(P/w)+
V2/2g
(in cm)
1.
2.
3.
4.5.
6.
7.
8.
9.
10.
11.
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