Chemical Engineering - Fluid Statics

Please help with all parts

1a) A tube is bent at 90, as shown below. The horizontal end of Length L = 10 cm is closed but the vertical end is open to the atmosphere. A fluid of SG = 1.4 fills the tube to a height of H = 10 cm. The tube is rotated about the vertical axis at a rotational speed, = 20!". Find the gage pressure Pg inside the tube at the closed end.

1b) Using a force balance, derive a relation for the pressure difference P inside and external to a cylindrical liquid jet of radius r, with liquid density and surface tension ; (b.) find the gage pressure Pg inside a cylindrical water jet of radius 0.5 mm ( = 0.07 ) in 1 atm air; (c.) what water drop radius would have the same Pg?

1c) Capillarity helps carry water and dissolved nutrients to upper parts of plants. Estimate the height water could rise in a tree thru tiny tubes of radius 0.0026 mm; for water, take = 0.07 and a constant angle = 15.

1d) A 1-m-diameter cylindrical mass, M, is connected to a 2-m-wide rectangular gate as shown in Fig. P2.80. The gate is to open when an unknown fluid (with SG = 1.4) level, h, drops below 2.5 m. Determine the required value for M and the the cable tension T. Neglect friction at the gate hinge and the pulley.