Concept explainers
Darcy’s law gives us the volume flow rate—volume per time (for example, cubic meters per day, m3/day). Another way to express volume is on a per-unit-area basis. For example, if we have a 1-m3 cube, we know its base is I m2—the cross-sectional area of the cube—and its height is 1 m. If we fill the cube with water, we can say we have 1 m of water per unit area. Darcy’s law can be rearranged to calculate the volume flow rate per unit area. This is called the specific discharge, which has units of length per time (for example, meters per day, m/day). Completing parts (a) through (c) will illustrate how specific discharge is related to the volume flow rate. (Hint: Assume that the units for hydraulic
- (a) Suppose 1 m3 of water is pumped from a well into an empty cylindrical tank. If the water level is 2 m above the base, what is the cross-sectional area of the tank? (Hint: Volume of a cylinder = πr2b = area of base X height.)
- (b) If it takes half a day to pump the 1 m3 of water into the tank, what is the flow rate in terms of both volume per unit time and specific discharge?
- (c) Write Darcy’s law so that it calculates the specific discharge.
Want to see the full answer?
Check out a sample textbook solutionChapter 22 Solutions
Conceptual Physical Science (6th Edition)
Additional Science Textbook Solutions
The Cosmic Perspective (8th Edition)
Conceptual Physics (12th Edition)
Physics: Principles with Applications
College Physics
Life in the Universe (4th Edition)
Cosmic Perspective Fundamentals
- If 200 oak trees are counted on a 2 km x 2 km patch of land, what is the density of maple trees per square kilometer? What is the density of the oak trees per km2?arrow_forwardthe average human body contains approximately 5 liters of blood. if the blood has a density of 1060 kg/m^3, what is the total mass of blood in the average human? note 1L =1000 cm^3.arrow_forwardA trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet. ft3 min 3 ft 12 ft 3 ft (a) If water is being pumped into the trough 2 cubic feet per minute, how fast (in ft/min) is the water level rising when his 1.2 feet deep? 5/48 x ft/min (b) If the water is rising at a rate of 3/8 inch per minute when h=2.5, determine the rate (in ft/min) at which water is being pumped into the trough. X ft/min 0.9arrow_forward
- DEA agents watch drug smugglers load cocaine onto a fishing boat in a Mexican river to transport it down the river to the ocean, and then to Miami. To estimate how much cocaine was loaded, they measure how much further the boat sinks into the water after being loaded. If the boat’s area at the waterline is 50 m2 and it sinks by 2 cm, how much cocaine was loaded?arrow_forwardThe volume of air in one beach ball is 972? in3. What is the volume of air in a ball whose radius is 3 inches greater than the first beach ball? A beach ball is spherical in shape. Recall that the formula for the volume V of a sphere where r is the radius is given by the following formula. V=4/3?r3 It is given that the volume of the first beach ball is 972? in3. Substitute this value for V in the volume formula for a sphere. ______= 4/3?r3arrow_forwardEarth’s density is about 5520 kg/m3 . Determine the density in g/cm3 by unit conversion.arrow_forward
- If a liquid has a mass density of 1350 kg/m3. a) What would be the weight density of the liquid in Newtons per cubic meter? b) What would be the weight density of the liquid in pounds per cubic foot?arrow_forwardA conventional oil barrel (cylindrical in shape) has an internal diameter of 22 inches and a maximum external diameter of 23 inches. The height inside the barrel is 33 inches, with a maximum external height of of 34 inches. if only 92% of the volume of the barrel can be filled, what is this volume in liters?arrow_forwardYou wish to calculate the average density of a substance, based on five density measurements. The density values are: 2.810 g/cm³, 2.78 g/cm3, 2.80 g/cm³, 2.9 g/cm³, and 2.83 g/cm3. How should you report the average density of the substance?arrow_forward
- The surface area of Earth is 510 × 106 km2, and 71% of this is ocean. Using the data from the sample exercise, calculate the average depth of the world’s oceans in feet.arrow_forwardThere is 2 m^3 of some gas with density 0.9 kg/m^3 The volume of gas was increased by factor of 2, What is the density now? Calculate answer to two decimals.arrow_forwardDensity is always expressed as mass per unit volume. If an organic liquid has a density of 0.9 grams per cubic centimeter and if 1 cubic feet is 7.481 gallons, How many cubic feet are needed to hold 1000 pounds of the liquid? how many gallons?arrow_forward
- An Introduction to Physical SciencePhysicsISBN:9781305079137Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar TorresPublisher:Cengage Learning