Question

6-7. Oil flows through the 100-mm-diameter pipe with a velocity of 8 m/s. If the pressure in the pipe at A and B is assumed to be 60 kPa, determine the x and y components of force the flow exerts on the elbow. The flow occurs in the horizontal plane. Take ρο -900 kg/m3 8 m/s 30° 100 mm 100 mm

Answer 1

Given : Pressure in the bibe at A and B :- 3 = 60 kPa velocity of oil thorough pipe (v) = 8 m/s Diameter of bibe. (d) = Joo mm Density of ail (lo) = goo kg/m3 v=& mise V=smis VR30 Asien of bibe! A = 74d2 = /2 (0-1)2 A = 0.007854 m2 ss Flow rate: Q = AV = (0.007854) (8) Q = 0.06283 m3/s

Now, applying Linear momentum equation across the contoral valume enclosing points Afb:. Along harizontal disth!. EFX = 0 + (VA) (-2) + VB PCO) - Fx + PA (A) – POCA) Cos 30º = P Q (CVB)x - VA) where, (ve)x = V Cos 30 Substituting values ; - Fx + 160x100) (0.007854) - (60x103) (0-007854) Cos 30° = 300 (0-06283)(8 cod 30 - 8) der Fx = 123.74 N 1 → all Horizontal component of force exerted on the elbow. Along vertical dich!. EFY = 0 + 0 + (vb)y (-a) 031 - Fy + PR(A) Sin 30º = (VB)y P(-2) Where (Ve)y = v sin 30°

Substituting values ; - Fy + 160x103) (0.007854) Sin 30 = ( 8 Sin 30') x 900 m. (-0.06283) or, Fy = 461.81 N → Vertical component of force exerted on the elbw.