Question 2 (cont'd) (b) As shown in Figure 2.3, a liquid of density p flows upwards against gravity through a contraction. The vertical height of the contraction is B. The liquid pressure, flow velocity and cross sectional area at the contraction inlet (Station 1) are P, V₁ and A₁, respectively, whereas the liquid pressure, flow velocity and cross sectional area at the contraction outlet (Station 2) are P₂, V₂ and 4₂, respectively. Assume that the liquid is inviscid and the flow is steady. A U-tube manometer is used to measure the difference in pressure between Stations 1 and 2. The manometer contains a liquid of density 1.2p, and the difference in liquid levels in both limbs of the manometer is H. (i) (ii) Obtain an expression for the pressure difference (P₁-P) between the contraction inlet and outlet solely in terms of the quantities p. g. B. Vi, A₁ and 4₂. Obtain an expression for the difference in liquid levels in both limbs of the manometer H solely in terms of the quantities V₁, g. 4₁ and 4₂ P2 V₂ (2) A2 ↓₂ 254 B A₁ Pipe- Flow Contraction Manometer 1.2p Figure 2.3

The flow between two horizontal infinite parallel plates is a two-dimension, steady-state, incompressible and fully- developed flow. The distance between the plates is h m. The bottom plate is stationary and the top plate velocity is U. m/s in the x-direction. The flow is driven by the top moving plate and there is, therefore, no pressure gradient in the direction of the flow. Velocity in the y-direction, v = 0. Note: Align the x-axis to the bottom wall. Use the x-momentum equation to show that the velocity profile equation is (a) u(y) = ay + b and find the values of a and b. Use the energy equation to derive the temperature distribution T(y) for the flow if the surface temperature and temperature gradient on the bottom plate are both zero. (b)

A turbine model has the following characteristics: Effective power: 13, 6 kW; Rotor Diameter: 0.38 meters, Flow: 0.34 ms, Energy Jump: 26.5 J / Kg and 3 R.P.S. rotation It is desired to construct a geometrically similar 1.20 meter diameter turbine that provides a power on the 656 kW axis, we ask: to calculate and justify its answers: a) the specific rotation; b) the unit quantities (rotation, flow and power); c) the rotation, flow and power of the model (bi-unit quantities).

If 10 m^3 of atmospheric air at 1 degree centigrade temperature are compressed to a volume of 1m^3 at 100°C, what will be the pressure of air?

FLUID MECHANICS 1