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Department of Civil Engineering and Applied Mechanics McGill University CIVE327 FLUID MECHANICS AND HYDRAULICS Assignment No. 1 1. What is the fractional volume change of 2 m3 of water at 20oC due to an applied pressure of 10 MPa? (see PWR 1.53) 2. The change in volume of a liquid with temperature is given by (∆V ) = α T V (∆T ) , where α T is the coefficient of thermal expansion. For water at 40oC, α T = 3.8 × 10 −4 K–1. What is the volume change of 1.5 m3 of 40oC water if ∆T = – 25oC? What pressure change would be needed to cause that same volume change? (see PWR 1.57) 3. A valve is closed in 4 s at the downstream end of a 3000-m pipeline carrying water at Vo = 2 m/s and c = 1000 m/s. What is the peak pressure developed by the closure? 4. A valve is closed at the downstream end of a pipeline in such a manner only one-half of the line is subjected to maximum pressure. During what portion of the time 2L/c is it closed? L is the length of the pipeline and c the wave speed.

Water

Valve Vo

5. For the tank shown in Fig. P2.38, if H = 16 cm, what will the pressure gage read? (see PWR 2.38)

Air H 4m

Water Hg

Figure P2.38

6. Find the absolute pressure in the water pipe shown in Fig. P2.40. The pressure at the other end of the manometer is atmospheric, 101 kPa. (See PWR 2.40) S = 0.8

Water

5 cm 5 cm 7 cm

10 cm Hg

S = 1.59

Figure P2.40

7. If atmospheric pressure at the ground is 14.7 psia (101.3 kPa) and temperature is 59oF (15oC), calculate the pressure 25000 ft (7.62 km) above the ground, assuming (a) no density variation, (b) isothermal variation of density with pressure, and (c) adiabatic variation of density with pressure. (See PWR Ex 2.1 and Ex 2.2)