A 45° reducing bend is connected in a pipe line the
diameter at the inlet and outlet of the bend are 600mm and 300mm respectively. Find the force
exerted by the water on the bend. If the intensity of
pressure at inlet to bend is 8.829N/cm2 and rate of
flow of water is 600 lit/sec.
Answers
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Explanation:
Solution:
Diameter at section 1 (d1) = 600mm = 0.6m
Area at section 1 (A1) =
= 0.2827m2
Diameter at section 2(d2) = 300mm = 0.3m
Area at section 2 (A2) =
= 0.07068m2
Discharge (Q) = 0.9 m3
/s
Velocity at section 1 (V1) =Q/A1 = =0.9/0.2827 = 3.18 m/s
Velocity at section 2 (V2) =Q/A2 =0.9/0.07068 = 12.73 m/s
Pressure at section 1 (P1) = 200Kpa = 200000N/m2
Force exerted by water on reducer =?
Applying Bernoulli’s equation between 1 and 2 (Z1 = Z2)
P2 = 124030 N/m2
∑
(
) (
)
(
) (
)
(
) (
)
( ) ( ) = 39178 N
The forces in the Y-direction will balance each other and Fy = 0.
Hence the force exerted by water on reducer is 39178 N to the right.
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