problem) A circular steel gate controls flow from a dam’s pool into an irrigation canal system’s raceways. When closed, the gate is in the vertical plane. It is hung in the dam’s concrete structure and controlled with a shaft that runs along the horizontal centre line of the gate. The gate can be opened (or closed) as a rotational motion about its horizontal centre line, by applying a moment on the shaft…

The gate is 2 meters in diameter. When the reservoir behind the dam is full (i.e. at design pool depth), the horizontal centre line of the gate is 3.8 meters below the water surface.

i) Determine the necessary moment that must be applied to the gate’s centreline shaft to keep it closed at design pool depth.

ii) Provide an opinion. Which is “BIG” and which is “small?” The moment or torque needed to keep the gate closed or the reaction forces in the dam wall where the shaft is anchored, and why..

problem) Water flows from a constant head water supply tank through a 36’ run-of-pipe and then exits from a spigot into the air. The water surface in the supply tank is 8 feet above the outlet of the spigot. A pick-up truck with a 200 gallon tank for hauling potable water is under the spigot. The 2” diameter new, commercial steel pipe (see White, pg. 371) is screwed together (threaded pipe), and contains the following fittings: one sharp edged inlet (White, pg. 393), four regular 90 degree elbows and one fully open angle value (White, pg. 391). The pipe supplier indicates that at nominal operating discharges a pipe friction factor of 0.023 is appropriate.

i) How long will it take to fill the water tank in the truck?

ii) Without actually performing the analysis, what are you motivated, as a good and diligent engineer, to double check at this point and why..?

problem) A hydropower development is being considered for a mountainous, rural province in south-central China. Almost all of the full run-of-river baseflow (7.0 cms), will be diverted and passed into a circular steel penstock. This penstock will be constructed of older, salvaged riveted steel pipe (see White, pg. 371), 300mm in diameter. The penstock will be 2.18 kilometers in length from the river diversion to the powerhouse. The diversion inlet is 800 meters above the power house.

i) If one were to ignore losses, what is the hydraulic power in Watts, Kilowatts, Megawatts and Horsepower that this facility is capable of producing..?

ii) What is the hydraulic power potential, in these same units, for this facility if pipe losses over the run of pipe that makes up the penstock are included? Your pipe friction factor is not given, a priori. You must demonstrate explicitly that the friction factor you ultimately settle upon for use in this analysis is accurate and correct for this pipe and its operating flow velocity. 

iii) A modern, high-tech bulb-turbine will be used for power generation. The effective diameter available for flow, after taking into account the area of the turbine blades and center-line bulb is 195mm. What is the average flow velocity thru the turbine section itself?

iv) Does this seem “fast”? At these velocities, would you expect hydraulic forces on the turbine blades and bulb to be small or large, qualitatively speaking, and what, specifically, would be causing them?

v) How many average “American” homes could be power with this facility?

vi) How many rural homes, typical of south central China could be powered with this facility?

problem) In a large scale commercial brewery, beer at 68 degrees (Fahrenheit) passes thru a 180 degree reducing bend in what is otherwise a continuous pipe. The system operating discharge is 3.0 cfs. The bend is in the horizontal plane and its weight is supported from below. The reducing bend is attached at its inlet and outlet sections with bolted flange fittings. The inlet diameter is 6 inches. The outlet diameter is 3 inches. Gage pressure at the 6 inch section is 16 psi. 

i) Find the net (make your frame-of-reference obvious with a sketch) force thatmust be restrained by the flange bolts. Use an analysis that does not include frictional losses as the beer passes through the reducing bend.

ii) Are the bolts in compression or tension?

iii) There are two dominant processes that are producing the forces that the bolts must resist: pressure-area forces and momentum flux (the “thrusts”) forces due to the fluid’s motion and change of direction. Which, if either, are dominating?

iv) If you had used an analysis that included frictional losses, would the net component force to be restrained have been less than or greater than that which you find outd and why (short of a complete recalculation, be specific – which terms of the analysis would change, how would they change and how would that effect the final answers with respect to the hydraulic forces in need of restraint)?

v) Given your answer to d.), above – was your choice of an analysis that did not include frictional losses, leading to the bolt forces, a “conservative” engineering choice?

problem) An excavated earthen channel is reasonable approximated as a rectangular section with a 20’ wide floor. Its floor and side slopes are covered with stones and cobbles. The channel’s slope is 0.008. Design flood discharges are anticipated to be in the range of 860cfs. For both the maximum and minimum estimates of roughness n (see White, pg. 709) for a stony/cobbles excavated earthen channel, determine the following:

i) The normal depths of flow for this channel section.

ii) The critical depth(s) of flow for this channel section.

iii) Is the flow super-critical or sub-critical?

Because of concerns about how close the normal depth of flow at 860cfs is to an overbank condition, the engineers decide to evaluate reducing the normal depth through this section of channel by lining it with finished concrete. In this design scenario, again using the maximum and minimum estimates for n (from White, pg. 709) for finished concrete, determine the same suite of parameters:

iv) The normal depths of flow.

v) The critical depth of flow.

vi) Has the critical depth changed over that of the earth lined channel, above?

vii) Is the flow super-critical or sub-critical in this scenario?

You almost certainly used the assumptions inherent in uniform flow to perform this analysis?

viii) What kinds of changes in channel characteristics (named all of them, specifically), over what upstream channel distances would make you problem the validity of these assumptions that have underpin your analysis?