You are working in a food production plant. Olive oil is being puped froun a sto

Question

You are working in a food production plant. Olive oil is being puped froun a storage tank to a mivear through a series of pipes and pups, as seen in the schematic below. At two points in the flow (point 1 and point 2) the pressure is measured through the use of manometers that are open to the atmosphere. by the three pumps and mechanical energy is being removed from the flow by friction losses. At point 1 the diameter of the pipe is 30 cm and the velocity of the fluid is 212 ms. At point 2 the pipe diameter is 15 cm. The height of olive oil in both manometers is 1.5m with point 1 being located2 m higher than point 2. The density of olive ol is 800 gmand the viscosity is 0.81 Pa. Mechanical energy is being added to the fiow storage point 2, where , represents the conmbined shaft wark of the three pumps and F (13 marks) (b) Is there a net gain or loss of energy in the flow between point 1 and point 2? Explain (2 marks) represents the frictional losses.

Explanation / Answer

(a) Discharge at the two points remain same,

So, A1 v1 = A2 v2

=> v2 = (A1 v1/A2) = ((pi x 0.32/4) x 2.12 / (pi x 0.152/4)) = 8.48 m/s

Applying Bernoulli's equation between points 1 and 2,

(P1/(rho x g)) + (v12 / 2g) + z1 - hL = (P2/rho x g) + (v22 / 2g) + z2

=> (1.5 x rho x g / (rho x g)) + (v12 / 2g) + z1 - hL = (1.5 x rho x g / (rho x g)) + (v22 / 2g) + z2

=> hL = ((v12 - v22 )/ 2g) + (z1 - z2) = ((2.122 - 8.482)/2g) + 2 = -1.436 m

Sum of shaft work and friction = 1.436 x g = 14.088 J/kg

(b) Since hL is negative, so there is net gain of energy in the flow between point 1 and 2. The energy added to flow by the pumps is more than the energy loss due to friction.

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