Legitimacy of Bernoulli’s Equation for liquid stream

OBJECTIVES

• To confirm tentatively the legitimacy of Bernoulli’s Equation for liquid stream like water.
• To record Pressure Measurements along a Venturi nozzle.

INTRODUCTION AND THEORY

As per the Bernoulli’s rule when region accessible for the liquid to stream decline at that point stream speed of the liquid increment and at the mean while time the liquid weight or the liquid potential vitality diminishes. This guideline was name after the Daniel Bernoulli who initially composes this standard in book named Hydrodynamic.

Following are a portion of the use of the Bernoulli’s standard

 Air-flight, Lift, Baseball, Draft, Sailing

Theory

As per Miller, R.W (1996), the conservation of energy law was the basic determining factor behind the deduction of the Bernoulli’s rule. Bernoulli’s rule express that the in a consistent streaming liquid the entirety of all the mechanical energies including active vitality, dynamic head, liquid weight and potential vitality ought to stay same at all the purpose of the stream. So in the event that any sort of vitality increment like on the off chance that motor vitality increment, at that point the other kind of the vitality like expected vitality, weight will diminish to make the last total same as in the past.

As indicated by the Bernoulli condition a streaming liquid have three things

 Pressure head

 Kinetic Energy

 Potential Energy

So we have

As indicated by conservation of energy law, energies at the info ought to be equivalent to the yield so

P_1/ρg+  (V_1^2)/2g+h=  P_n/ρg+  (V_n^2)/2g+h

Equations:

From Bernoulli’s guideline it very well may be expressed that the thickness and weight are contrarily relative to one another’s methods high thickness liquid will apply more weight while moving than the low thickness liquids.

In the level channel where the delta and outlet of the are at same stature, the z amount can be evacuated to give the above notice condition of Bernoulli’s guideline another look from where we can compute the tallness anytime of the stream on the off chance that we have the underlying tallness of stream and speed at particular positions.

P_1/ρg+  (V_1^2)/2g=  P_n/ρg+  (V_n^2)/2g

P_1/ρg=h1 and  P_n/ρg=hn 

h_1+  (V_1^2)/2g= h_n+  (V_n^2)/2g

h_n= h_1-[  (v_n^2)/2g-  (v_1^2)/2g]

APPARATUS

1. Bernoulli’s apparatus (Figure 1).
2. Hydraulic bench.

Figure 1. Bernoullis Appratus

METHODOLOGY AND PROCEDURE

1. Mastermind the experimentation set-up on the HM 150 with the end goal that the release courses the water into the channel.
2. Make hose association between HM 150 and HM 150.07
3. Open release of HM 150 .
4. Set top nut (1) of test pressure organ such that slight obstruction is felt on moving test.
5. Open delta and outlet valves.
6. Switch on siphon and gradually open primary chicken of HM 150.
7. Open vent valves (2) on water pressure measures.
8. Cautiously close outlet valve until pressure measures are flushed.
9. By all the while setting channel and outlet valve, regulate water level in pressure checks with the end goal that neither upper nor lower extend limit (UL, LL) is overshot or undershot.
10. Record pressures at all estimation focuses. At that point move overall. pressure probe to relating estimation level and note down by and large weight.
11. Decide volumetric stream rate. To do as such, use stopwatch to set up time t required for bringing the level up in the tank of the HM 150 from 20l to 30l.

DATA AND CALCULATIONS

Table 1 calculations data for the Bernoullis experiment

 RESULTS AND GRAPHS

Figure 2. Plot the V(Calculated) and V(measured) vs. Area(mm2)

Figure 3. Plot the h(static) and h(dynamic) vs. Area(mm2)

SAMPLE OF CALCULATIONS

V _calculated = Volumetric Flow rate (Q) M3/s / Area (m2)

= 0.00011765 / 338.6 x 10^-6 = 0.6264 m/s

H _dyn = H _total – H _stat

= 170-150 = 20

V _measured =

= x10^-3

= 0.3475 m/s

DISCUSSION

• From the calculation it is very clear that with increase in area of the flow velocity decrease and pressure increase.

• As shown in graph that the increase in area of flow decrease the height of water in manometer column means they are indirectly proportional to each other

• The difference between theoretical value and measured value it tends to be said that water isn’t a perfect liquid.

• Height of water in the final column was not equal to the initial values which show that there are friction losses in water particle.

• This type of information is very use full in the case if nozzles, jets and diffusers.

CONCLUSIONS AND RECOMMENDATIONS

The Aim of objective of this experiment was to verify experimentally the validity of Bernoulli’s equation for fluid flow.And to record Pressure Measurements along a Venturi nozzle. From the investigation it very well may be infer that with decline in region of stream there is an expansion in speed and lessening in the stream weight of the liquid.

REFERENCES

·        R.k. bansal (n.d) chapter 8 flow measurement, a textbook of fluid mechanics

·        Miller, r.w (1996) flow measurement engineering handbook 3rd ed. Mcgraw-hill book, new york n.y

·        Usbr (1996) flow measurement manual. Water resource publication llc highland ranch co

DATA APPENDIX/ DATA WORKSHEET

Given data:-