a$.$ Explain what is meant by forced vortex and derive the expression for the radial

pressure distribution in forced vortex. $(5$ marks$)$

b$.$ Explain the basic principle involved in measuring pressure and pressure difference

using manometers. Indicate when the use of manometers is advantageous. $(8$ mark

c$.$ A U$-$tube manometer has both its limbs enlarged to $25$ times the tube area. Initially the

tube is filled to some level with oil of specific weight ${}_m.$ Then both limbs are filled

with fluid of specific weight ${}_s$ to the same level, both limbs being exposed to the

same pressure. When a pressure is applied to one of the limbs the manometric fluid

rises by h m $.$ Derive an expression for the pressure difference in the limbs$.$ In both

cases assume that the liquid level remains in the enlarged section. $(12$ marks$)$