A mercury manometer is attached to a section of the pipe shown in the figure. Mercury levels are indicated when there is no water flowing through the pipe. When water starts flowing through the pipe continuously at constant rate in the direction of the arrow, the level of mercury at $$B:$$

A jet of water (area $${A_j},$$ velocity $${V_j},$$ density $$\rho $$ ) impinges horizontally on a curved vane which deflects the jet through $${60^0}$$ upwards. If the vane travels horizontally at a speed $$'u'$$ find
(a) the force experienced by the vane, and
(b) the power developed by the vane.

Axial operation claw clutches having self-locking tooth profile

The expected life of a ball bearing subjected to a load of $$9800N$$ and working at $$1000RPM$$ is $$3000$$ hours. What is the expected life of the same bearing for a similar load of $$4900$$ $$N$$ and a speed of $$2000rpm$$