(b) Euler's equation

(a) Navier-Stoke equation

(c) Newtonian fluid (5%) (5%)

(a) A reservoir manometer is built with tube diameter of d and a reservoir diameter of D. The density of liquid through the manometer is p. Derive an equation for the pressure difference (P1 - P2) in terms of (p, g x2, d, D). (8%)

(b) If the manometer liquid is oil with specific gravity of 0.8, d = 10 mm, and D = 30 mm, calculate the pressure difference in unit of SI. (5%)

3. Water flows under a sluice gate on a horizontal bed at the inlet to a flume as shown. The water depth of the upstream and the downstream of the gate is 2.4 m and 0.2 m, respectively. The flow may be considered to be frictionless, uniform at each section. Calculate the flow speed, upstream and downstream of the gate. (10%)

4. Water flows in an open channel of a trapezoidal shape at a normal depth of 1.6 m. The bottom width is 3.2 m and the sides slope at 1:1 (45°). The flow rate is 8.2 m3/sec. The channel wall is smooth, uniform earth with a Manning roughness coefficient (n) of 0.022. Find the bed slope. (12%)

(a) The viscous torque produced on a disc rotating in a liquid depends upon the characteristic dimension D, the speed of rotation n, the density ρ and the dynamic viscosity p. Show the dimensionless equation linking these quantities. (10%)

(b) In order to predict the torque on a disc 0.5 m diameter which rotates in oil at 200 rpm, a model is made to a scale of 1/5. The model is rotated in water. Calculate the speed of rotation for the model which produces dynamic similarity. (Oil's density and dynamic viscosity are 750 kg/m3and 0.2 N-s/m2, respectively; water's density and dynamic viscosity are 1000 kg/m3 and 0.001 N-s/m2, respectively) (10%)

(c) When the model is tested at 18.75 rpm the torque was 0.02 N-m. Predict the torque on the full-size disc at 200 rpm. (5%)

(a) Solve for the velocity field.

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