BERNOULLI EQUATION

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BERNOULLI EQUATION




An approximate relation between pressure, velocity and elevation and valid in regions of steady, incompressible flow where net frictional forces are negligible. In simple way to understand, to know the relationship between pressure and fluid velocity in the flow system.

Despite its simplicity, it has been proven to be very powerful tool in fluids mechanics which fluid motion is governed by the combined effects of pressure and gravity forces. There are 3 types main energy in the moving fluid which are:
  • ·     Potential energy, energy which possessed by fluid based on potential head (the height at point in fluid flow measured from datum or reference line).

Penergy = Z (m)
  • ·    Kinetic energy, energy possessed by the fluid particles based on it velocity.

Kenergy = v 2 / 2g (m)
  • ·    Pressure energy, energy possessed by fluid based on the pressure in the fluid.

P = ρgh
Therefore, h = P / ρg


BERNOULLI THEOREM APPLICATION

  •     Flow through Uniform Pipe (meter, m)

H =P/ρg+  (v2 )/2g+Z

  •      Flow through Tapered Pipe

·         The fluid flowing concept in a uniform pipeline can be also used in a pipeline with different diameter.

  •      Flow through Ventury Meter, (unitless)

Q=A√(2gH/((m^2-1)))

Q=Cd A√(2gH/((m^2-1)))


CALCULATION

1. Water is flowing through a pipe with diameter of 150mm and 200mm at the bottom and upper end respectively. The intensity of pressure at the bottom end is 200Pa and the pressure at the upper end is 300Pa. Determine the difference in datum head if the rate of flow through pipe is 0.05m3/s.

Solution:

Given,
Ø1 = 150mm = 0.15m, Ø2 = 200mm = 0.2m, Q = 0.05 m3/s
P1 = 200Pa, P2 = 300Pa, A = πd2/4

a.    Find each velocity,

                                    Q = AV

0.05 = (π 〖(0.15)〗^2)/4 . v1
V1 = 2.829 m2/s
0.05 = (π 〖(0.2)〗^2)/4 .v2
V2 = 1.59 m2/s

b.    Use Bernoulli Theorem, to find the difference in datum
H = P/ρg+ (v2)/2g+Z

P1/ρg+ 〖v1〗^2)/2g+Z1=P2/ρg+(〖v2〗^2  )/2g+Z2

200/9810 + (〖(2.829)〗^2  )/(2(9.81))+Z1=300/9810+  (〖(1.59)〗^2  )/(2(9.81))+Z2

Z2 - Z1=0.269 m

2. A sharp around the orifice of 50mm diameter water out of a tank. Column of water in the tank is 4.5m. find the coefficient of discharge if its discharged is 11.45 x 10-3 m3/s.

Solution:

Q=Cd A√2gh

〖11.45×10〗^(-3)=Cd (  (π 〖(0.05)〗^2)/4)√(2(9.81)(4.5))

Cd=0.62

ABOUT US

We are students of Bachelor Degree of Civil Engineering Technology (Environmental) with Honours from University Tun Hussein Onn Malaysia. Our teammates are:

1. MUHAMMAD AFIQ BIN ZABIDI (AN170093)

2. MUHAMMAD ARIF RIDZUAN BIN MD KHALIL (AN170061)

3. NUR IZZAH BINTI MOHAMAD KETAR @ MOKHTAR (AN170125)

4. NUR LAILA BINTI OSMAN (AN170083)

5. NUR IZZMIRZA BINTI MOHSIN (CN170013)

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