Hydraulics

Question ( 2- 26 ) , MCQ 2 Simplity the Navier-Stokes equation as much as possible for the case of incompressible hydrostatics, with gravity acting in the negative z-direction. Begin with the incompressible vector form of the Navier-Stokes equation and identify the final vector equation.

Question 3 A town's water system is connected to a supply reservoir, reservoir A, that feeds into the town at a single junction J, as shown in the figure. The water is distributed to two key zones shown as B and C on the figure. Nodes A, B and C are connected to the junction by pipes. The water levels in A and Care, respectively, 300 m and 180 m AOD. Pipe lengths, diameters and friction factors are given in the table below. (a) What is the maximum water level that can be maintained at B to ensure that any flow is form J to B? A proposal to develop the town requires a new out-take to be provided from J to D. The design discharge from J to D, measured directly at J, is 35 Ls¹. The water level in B is 250 m (b) Discuss, with the appropriate evidence and supporting calculations, how this will impact the existing system, and if zone B will still be provided with water from the supply reservoir.

Objective This exercise allows us to observe the load losses of a current that circulates through a widening of 25/40 mm.

Q1. A rectangular channel b= 1.5m , Q= 900L/s, the depth of flow before the hump is 1m and Az=200mm , compute the depth of flow above the hump.

Q2. A rectangular channel b= 2.0 m, Q= 2 m3/s, the depth of uniform flow before the hump is 0.8 m. What should be the height of the hump (Az) to have critical flow over it (no head loss).

An existing trapezoidal aqueduct (b= 15 ft, S = 0.01%, n = 0.025) with a 34:1 side slope was designed to flow at D/b = 0.30. The channel is sides and bottom are modified to increase side slope to 2½:1 and decrease roughness to 0.021. Calculate percent change in flow capacity assuming base width, slope and design D/b remain constant.

8. (5 points) Please describe combustion, gasification and pyrolysis. What are the differences?

Q1. Calculate capillary rise/fall in a glass tube 2 mm diameter when immersed in (a) water (b) mercury.Both the liquids are at 20°C and the surface tension values at this temperature for water and mercury are 0.072 N/m and 0.052 N/m respectively. The specific gravity of mercury is 13.6. The contact angle of water and mercury are 0° and 130° respectively.

Q2. A 75 m long cast iron pipe, 15 cm in diameter, connects two tanks (open to the atmosphere) that have a water surface elevation difference of 5 m. The entrance of the pipe from the supply tank is square edged, and the pipe contains a 90° bend with a sharp, 15 cm radius. Determine the flow rate in the \text { pipe. Use } f=\frac{0.25}{\left[\log \left(\frac{e / D}{3.7}+\frac{6.71}{N \cdot 9.9}\right)\right]^{2}}

Water flows smoothly and falls on top of a plat surface (anupside-down baking tray in the picture). Two interestingphenomena are involved here: A) vena contracta; and B)hydraulic jump. Google these terms and choose one to study inyour video: A) Explain phenomenon A in the picture. Study water column diameter versus z position based on mass conservation. Make it quantitative. Compare your theory with your own experimental measurements. B) Explain phenomenon B in the picture. Study the diameter of the circle on the flat surface versus flow rate based on mass conservation. Make it quantitative Compare your theory with your own experimental measurements.