A mother wants to make annual deposits for 12 years in order to prepare withdrawals of PhP15,000.00 each year for four years. The said withdrawals will start at the end of the 16th year. If money can earn a simple interest of 8% per annum, how much shall be the expected money she needs to earn at the beginning of the 16th year?

Amixture of slurry and mud is to be pumped through a horizontal pipe of diameter 500 mm. the fluid behaves as a bingham plastic with a yield stress of 30 pa and viscosity 0.04 pa.s. describe the effects of the shear stress through a transverse section of the pipe by plotting the variation in shear stress and velocity profile: (i) just before the slurry starts to move (ii) as the slurry flows when the pressure gradient is double that in part (i)