A conical tank of radius R and height H, pointed end down, is full of water....
A conical tank of radius R and height H, pointed end down, is full of water. A small hole of radius r is opened at the bottom of the tank, with r, much much less than, R so that the tank drains slowly. Find an expression for the time T it takes to drain the tank completely.
Hint 1: use Bernoulli’s equation to relate the flow speed from the hole to the height of the water in the cone.
Hint 2: start with a (mathematical) statement about the volume flow rate at the hole of radius ‘r’.
Answer: 
Homework Answers
Add Answer to:
A conical tank of radius R and height H, pointed end down, is
full of water....
A cylindrical tank (height h, radius r) is full to the brim of water and its...
A cylindrical tank (height h, radius r) is full to the brim of water and its top is open to the outside air. What expression describes the speed of fluid flowing out of a hole that is opened up at height h′ above the bottom of the tank?
Problem 4 4.50 A conical flask contains water to height H=36.8 mm, where the flask diameter...
Problem 4 4.50 A conical flask contains water to height H=36.8 mm, where the flask diameter is D = 29.4 mm. Water drains out through a smoothly rounded hole of diameter d= 7.35 mm at the apex of the cone. The flow speed at the exit is approxi- mately V = V2gy, where y is the height of the liquid free surface above the hole. A stream of water flows into the top of the flask at constant volume flow...
Suppose a conical tank (think of an ice cream cone, point down) has a capacity of...
Suppose a conical tank (think of an ice cream cone, point down) has a capacity of 7 gallons, and that 3 gallons of water are in it already. Water is added at a rate of 6 gallons per minute, but the cone springs a leak near its tip after 10 seconds. Water exits the tank at a rate determined by Torricelli's Law, v2gh (where v is the linear velocity of the water, g the acceleration due to gravity, and h...
To empty if c 0.6? See Problem 13 in Exercises 1.3. 13. Leaking Conical Tank A tank in the form o...
to empty if c 0.6? See Problem 13 in Exercises 1.3. 13. Leaking Conical Tank A tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. 16. H 75 (a) Suppose the tank is 6 m high and has radius 3 m and an the circular hole has radius 5 cm. In Problem 14 in Exercises 1.3 you were asked to derive the differential equation governing the...
(3 points) A tank of diameter D is filled with water up to a height h...
(3 points) A tank of diameter D is filled with water up to a height h above the bottom of the tank (Figure 3). At the bottom of the tank is a hole of diameter d. Assume that the water flows out of the hole with a laminar flow and that the difference in atmospheric pressure between the top and the bottom of the tank is negligible. Figure 3: A tank draining (c) If you no longer assume that the...
The tank pictured in Figure 2 with height H and diameter D contains water, which drains through a small round hole with diameter d. Torricelli’s law states that the average velocity v of the draining...
The tank pictured in Figure 2 with height H and diameter D
contains water, which drains through a small round hole with
diameter d. Torricelli’s law states that the average velocity v of
the draining water is , where g
is the acceleration of gravity and h the water level. Derive an expression to
describe the time taken for the tank to drain, if it is initially
full of water. Future interplanetary astronauts could use the tank
as a simple...
A large cylindrical tank with diameter D is open to the air at the top. The...
A large cylindrical tank with diameter D is open to the air at the top. The tank contains water to a height H. A small circular hole with diameter d<< D is then opened at the bottom of the tank. Ignore any viscosity effects. (a) Find the height y of water in the tank as a function of time t after the hole is opened. (b) If the initial height H of the water is doubled, by what factor does...
A cylindrical water-storage tank has a height of 8.3 m and a radius of 5.8 m....
A cylindrical water-storage tank has a height of 8.3 m and a radius of 5.8 m. The storage tank is full of water but is vented to the atmosphere. The bottom of the tank is 33 m off the ground. A 14 cm diameter pipe runs vertically down from the tank and goes 1.5 m underground before turning horizontal. The water flow in the horizontal pipe is 79 L/s. A) What is the water pressure (gauge) in the horizontal pipe...
Draining of cylindrical tank. You have a cylindrical tank full of water with a diameter =Dtank....
Draining of cylindrical tank. You have a cylindrical tank full of water with a diameter =Dtank. The height (htank) is changing with time. You are draining the tank through a hole in the bottom. The hole has a diameter Dhole. The velocity of the water leaving the tank depends on the height of the water and can be given as: v2 = 2 g htank. When the hole is first opened, the height of the water is ho. Draw and...
3. (3 points) A tank of diameter D is filled with water up to a height...
3. (3 points) A tank of diameter D is filled with water up to a height h above the bottom of the tank (Figure 3). At the bottom of the tank is a hole of diameter d. Assume that the water flows out of the hole with a laminar flow and that the difference in atmospheric pressure between the top and the bottom of the tank is negligible Figure 3: A lank draining a) What speed will the water have...
Problem 4 4.50 A conical flask contains water to height H=36.8 mm, where the flask diameter is D = 29.4 mm. Water drains out through a smoothly rounded hole of diameter d= 7.35 mm at the apex of the cone. The flow speed at the exit is approxi- mately V = V2gy, where y is the height of the liquid free surface above the hole. A stream of water flows into the top of the flask at constant volume flow...
Suppose a conical tank (think of an ice cream cone, point down) has a capacity of 7 gallons, and that 3 gallons of water are in it already. Water is added at a rate of 6 gallons per minute, but the cone springs a leak near its tip after 10 seconds. Water exits the tank at a rate determined by Torricelli's Law, v2gh (where v is the linear velocity of the water, g the acceleration due to gravity, and h...
to empty if c 0.6? See Problem 13 in Exercises 1.3. 13. Leaking Conical Tank A tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. 16. H 75 (a) Suppose the tank is 6 m high and has radius 3 m and an the circular hole has radius 5 cm. In Problem 14 in Exercises 1.3 you were asked to derive the differential equation governing the...
(3 points) A tank of diameter D is filled with water up to a height h above the bottom of the tank (Figure 3). At the bottom of the tank is a hole of diameter d. Assume that the water flows out of the hole with a laminar flow and that the difference in atmospheric pressure between the top and the bottom of the tank is negligible. Figure 3: A tank draining (c) If you no longer assume that the...
The tank pictured in Figure 2 with height H and diameter D
contains water, which drains through a small round hole with
diameter d. Torricelli’s law states that the average velocity v of
the draining water is , where g
is the acceleration of gravity and h the water level. Derive an expression to
describe the time taken for the tank to drain, if it is initially
full of water. Future interplanetary astronauts could use the tank
as a simple...
Draining of cylindrical tank. You have a cylindrical tank full of water with a diameter =Dtank. The height (htank) is changing with time. You are draining the tank through a hole in the bottom. The hole has a diameter Dhole. The velocity of the water leaving the tank depends on the height of the water and can be given as: v2 = 2 g htank. When the hole is first opened, the height of the water is ho. Draw and...
3. (3 points) A tank of diameter D is filled with water up to a height h above the bottom of the tank (Figure 3). At the bottom of the tank is a hole of diameter d. Assume that the water flows out of the hole with a laminar flow and that the difference in atmospheric pressure between the top and the bottom of the tank is negligible Figure 3: A lank draining a) What speed will the water have...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 11 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 11 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 11 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 11 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 11 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 11 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 11 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 11 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 11 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 11 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 11 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 11 months ago