To verify the Bernoulli's equation experimentally

Objective

To verify the Bernoulli’s theorem experimentally

EquipementInlet supply tank with overflow arrangement, outlet supply tank with means of varying flow rate, perspex duct of varying cross section and a series of ;piezometric tubes installed along its length.

Introduction and Theory:

Considering frictionless flow along a variable area duct, the law of conservation of energy states that for an inviscid, incompressible, irrational and steady flow along a stream line the total energy (or head) remains the same. This is called Bernoulli’s equation.

The total head of flowing fluid consists of pressure head velocity head and elevation head, Hence.

p ₁/γ + ν ²1/2g +z₁ = p₂/γ + ν ²₂/2g +z₂

Where P, V, and Z refer to the pressure, velocity and position of the liquid relative to some datum at any section.

Experimental Setup: The experimental set up consist of a horizonal perspex duct of smooth variable cross section of convergent and divergent tuype. The section is 40m x 40mm at the entrance and exit and 40mm x 20mm at middle. The total length of duct is 90cm. The piezometric pressure P at the locations of pressure tappings is measured by means of 11 piezometer tubes installed at an equal distance of 7.5 cm along the length of conduit. The duct is connected with supply tanks at its entrance and exit end with means of varying the flow rate.

Experimental Procedure:

Note down the piezometers distance from inlet section of the perspex duct

Note down the corss sectonal area of perspex duct at each of the piezometer tapping points.

The apparatus is levelled so that the datum head is treated as constant rthrough out the duct.

By maintaining suitable amount of steady head in the supply tanks, there establishes a steady non uniform flow in the conduit. Time is allowed to stabilize the level in the tubes.

The discharge flowing in the conduit is recorded together with the water levels in each piezomerter tubes.

This procedure is repeated for other values of total head in the supply tank and for other discharges.

Observations:If v is the velocity of flow at a particular section of the duct and Q is the discharge, then by continuity equation.

V = Q/ area of section

Observation and Computation sheets:

Area of collecting tank =

Increase in depth of water =

Time =

Discharge =

Area at inlet section = 40x40mm., Exit = 40x 40mm , Mid Sectio= 40x20mm

Tube No. 1 2 3 4 5 6 7 8 9 10 11

Distance

From inlet

Section (cm)

Area of

C/s of

Conduit

A(cm²)

Velocity

Of flow

(cm/sec)

V=(Q/A)

ν²/2g (cm)

p/γ + z(cm)

p/γ + z + ν²/2g (cm)

Graph to plot:Plot piezometric head (p/γ + Z ), velocity head (ν²/2g),total head (p/γ + z + ν²/2g) V/s distance if piezometric tubes from same reference point

Comment:Since the conduit is horizontal, the total energy at any section with reference to the center line of the conduit is the sum of p/γ and ν²/2g ,(here γis the wt. Density of the fluid and g is the acceleration due to gravity). One can compare the values of the total energy at different sections and comment about the constancy of energy in converging the diverging conduit.

Precautions:Apparatus should be in leveled condition

Reading must be taken in steady or nearby steady conditions. And it should be noted that water level in the inlet supply tank should reach the overflow condiiton.

There should not be any air bubble in the piezometers and in the perspex duct.

By closing the Regulating valve, open the control valve slightly such that the water level in the inlet supply tank reaches the overflow conditions. At this stage check, that pressure head in each pie3zometer tube is equal. If not adjust the piezometers to bring it equal.