The pressures at two sections of a horizontal pipe are 0.3 kgf/cm2 and 0.6 kgf/cm2 and the diameters are 7.5 cm, and 15 cm respectively. Determine the direction of flow if water flows at a rate of 8.5 kg/sec. State your assumptions.
Data:
P1 = 0.3 kgf/cm2
P2 = 0.6 kgf/cm2
D1 = 7.5 cm
D2 = 15 cm
Mass flow rate = 8.5 kg/sec
Formulae:
For the flow direction from 1 to 2,
\(\displaystyle \frac{p_1}{\rho_1g} + \frac{v_1^2}{2g}+z_1 = \frac{p_2}{\rho_2g} + \frac{v_2^2}{2g} + z_2 + h + w - q \)Calculations:
Volumetric flow rate = 8.5/1000 = 8.5 x 10-3 m3/sec
V1 = 8.5 x 10-3/(πD12/4) = 8.5 x 10-3/(π x 0.0752/4) = 8.5 x 10-3/0.00441= 1.924 m/sec
V2 = 8.5 x 10-3/(πD22/4) = 8.5 x 10-3/(π x 0.152/4) = 8.5 x 10-3/0.01767 = 0.481 m/sec
P1 = 0.3 kgf/cm2 = 0.3 x 9.812 N/cm2 = 2.9436 x 104 N/m2
P2 = 0.6 kgf/cm2 = 0.6 x 9.812 N/cm2 = 5.8872 x 104 N/m2
Assuming the flow direction is from 1 to 2:
2.9436 x 104/1000 + 1.9242/2 = 5.8872 x 104/1000 + 0.4812/2 + h + w -q
29.436 + 1.851 = 58.872 + 0.116 + h + w -q
In the given problem work done by fluid (w) and pump work on fluid (q) are zero.
So to balance the above equation, the quantity h has to have negative values. This is not possible.
The above equation will be a correct one, if the flow is from 2 to 1.
i.e. 58.872 + 0.116 = 29.436 + 1.851 + h
Therefore the flow direction is from the end at which pressure is 0.6 kgf/cm2 and diameter is 15 mm to the end at which pressure is 0.3 kgf/cm2 and diameter is 7.5 mm.
Last Modified on: 04-Feb-2022
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