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Classic49

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1. I am trying to help my grandson with his homework and I have to determine the flow of a fluid in a pipe. I am told that mass flow rate is 4Kg/s; density p is 1012Kg/m

2. I have applied Bernoulli's Equation, Continuity Equation and Mass Flow Rate but get different results so am not sure where I am going wrong.

3. Putting values into the Bernoulli equation, we have:

700 + (1012 x 9.81 x 0) + (½ x 1012 x V1

This simplifies to:

700 + 0 + (506 x V1

506 x V1

Therefore V1 = (V2 x A2)/A1 =( V2 x 0.1256)/0.07065 = 1.78 x V2

Putting the value of V1 into the Bernoulli equation above, I get

506 x (1.78 x V2)

This gives me

From the Continuity Equation,

4. The piece of information I have not used is the Mass Flow Rate. If I use the information in the equation

Mass Flow Rate = Density (p) x Area (A1) x Velocity (V1), I get V1 = 4/(1012 x 0.07065) = 0.0559 and

V2 = 4/(1012 x 0.1256) = 0.0315 which are widely different from the values calculated above.

5. I would be grateful for some guidance as to where I am going wrong.

^{3}; Diameters D1 = 300mm, D2 = 400mm; Pressure P1 = 700Pa, P2 = 600Pa; Heights y1=0mm, y2=100mm2. I have applied Bernoulli's Equation, Continuity Equation and Mass Flow Rate but get different results so am not sure where I am going wrong.

3. Putting values into the Bernoulli equation, we have:

700 + (1012 x 9.81 x 0) + (½ x 1012 x V1

^{2}) = 600 + (1012 x 9.81 x 0.1) + (½ x 1012 x V2^{2})This simplifies to:

700 + 0 + (506 x V1

^{2}) = 600 + 992.772 +(506 x V2^{2}), or506 x V1

^{2}= 600 + 992.772 - 700 +(506 x V2^{2}) = 892.772 +(506 x V2^{2})I need to determine V1 and V2 so I tried using the Continuity equation to establish a relationship between the two. From the gives diameters, Areas are A1 = 0.07065 m^{2}, A2 = 0.1256 m^{2}Therefore V1 = (V2 x A2)/A1 =( V2 x 0.1256)/0.07065 = 1.78 x V2

Putting the value of V1 into the Bernoulli equation above, I get

506 x (1.78 x V2)

^{2}= 892.772 +(506 x V2^{2})This gives me

**V2 = 0.902 m/s**From the Continuity Equation,

**V1 = 1.78 x V2 = 1.6 m/s**

4. The piece of information I have not used is the Mass Flow Rate. If I use the information in the equation

Mass Flow Rate = Density (p) x Area (A1) x Velocity (V1), I get V1 = 4/(1012 x 0.07065) = 0.0559 and

V2 = 4/(1012 x 0.1256) = 0.0315 which are widely different from the values calculated above.

5. I would be grateful for some guidance as to where I am going wrong.

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