Water (density ρ)is flowing through the uniform horizontal tube of cross-sectional area A with a constant speed v as shown in the figure. The magnitude of force exerted by the water on the curved corner of the tube is (neglect viscous forces)
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a
3ρAv2
b
2ρAv2
c
2ρAv2
d
ρAv22
answer is A.
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Detailed Solution
GivenDensity of water = ρCross-sectional area= AConstant speed= vAlong x and y directions along in momentum of water is P→i=mvj^Pf→=mv32i^-mv2j^∆P→=Pf→-Pi→=mv32i^-mv32j^⇒ΔP¯net=32mv2+-32mv2=3mvForce on bend is rate of change of momentum ⇒ΔF¯net=3dmdt.v=3ρAv2