wide. Water is filled to the top. Determine the factor of safety against sliding if the friction coefficient and concrete density is Royal Academy of Engineering 1. Calculate Dam Weight ( 2. Calculate Hydrostatic Force ( cap F sub h 3. Calculate Factor of Safety Against Sliding ( cap F cap S sub s The resisting force is friction: İstanbul Üniversitesi Conclusion: The dam is against sliding ( ) and requires a wider base or higher friction to be safe. Recommended PDF Resources
Fr1=189.81×0.8=187.848=182.8014≈6.425cap F r sub 1 equals the fraction with numerator 18 and denominator the square root of 9.81 cross 0.8 end-root end-fraction equals the fraction with numerator 18 and denominator the square root of 7.848 end-root end-fraction equals 18 over 2.8014 end-fraction is approximately equal to 6.425
Volume per day=0.01833 m3/s×86400 s/day≈1,583.7 m3/dayVolume per day equals 0.01833 m cubed / s cross 86400 s/day is approximately equal to 1 comma 583.7 m cubed / day
Built with massive concrete or masonry volumes. The dead weight of the structural material generates a downward gravitational force sufficient to keep the resultant force vector within the middle third of the dam’s base, preventing tensile stress and overturning.
: Use the depth of the centroid and the wetted area of the slope. Locate Center of Pressure : Use the formula to find where the resultant force actually acts. fluid mechanics dams problems and solutions pdf
Over time, silt collects at the bottom of the reservoir. This "sludge" has a higher density than pure water, increasing the hydrostatic pressure on the lower portion of the dam beyond original design specs.
cap W sub 2 equals gamma sub c center dot open paren one-half center dot base center dot height close paren equals 24 center dot open paren one-half center dot 14 center dot 24 close paren equals 4032 kN/m Total Weight (
During heavy rains, excess water must be released. Moving water carries immense kinetic energy.
A typical "dam problems and solutions PDF" will walk you through the calculation of the FOS for sliding, using the formula: FOS_sliding = µ * (∑ V - U) / ∑ H where ∑ V is the total downward vertical force (including the dam's weight), U is the total uplift force, ∑ H is the total horizontal force, and µ is the friction coefficient. Calculate Dam Weight ( 2
: The resultant hydrostatic force on a submerged gate must be balanced by structural hinges. Example 2 from a curved surface lecture shows a quarter-circular gate hinged at B. The force equation includes weight and water forces: F = 7483.5 lbs .
). The sequent depth relationship is defined by the Belanger equation:
A trapezoidal dam (concrete, ( \rho_c = 2400 , \textkg/m^3 )) has height 40 m, crest width 5 m, base width 30 m, water depth 40 m. Ignoring uplift, find FS against overturning about toe. (Hint: Divide trapezoid into rectangle + triangle, compute weights and moments) Answer: FS ≈ 2.1 (depends on exact geometry).
Accounts for water seeping under the dam, typically modeled as a triangular or trapezoidal pressure distribution. Example Walkthrough: Resultant Force on a Dam Recommended PDF Resources Fr1=189
The primary function of a dam is to impound water, which exerts immense hydrostatic pressure against the structure. If a dam is not properly analyzed for these forces, it risks catastrophic failure via overturning, sliding, or structural cracking. The challenge lies in accurately calculating the magnitude, direction, and specific line of action of the resultant hydrostatic force for both planar (gravity dams) and curved (arch dams) surfaces. The Solution
). This causes the fluid to vaporize, forming vapor bubbles. As these bubbles travel to regions of higher pressure, they collapse violently. The resulting micro-jets and shockwaves exert cyclic pressures up to several gigapascals, rapidly pitting and destroying concrete structures. Engineering Solutions Cavitation is managed by controlling the cavitation index (
cap W sub 1 equals gamma sub c center dot open paren width center dot height close paren equals 24 center dot open paren 4 center dot 24 close paren equals 2304 kN/m Triangular Part (
Knowing the water force is only the first step—engineers must verify the dam won't slide, overturn, or crack. Stability checks are critical for gravity dams.