Question

In: Civil Engineering

A 4 m-wide tank with height of 1.8 m filled with water is pulled with a...

A 4 m-wide tank with height of 1.8 m filled with water is pulled with a cable inclined at 30o to the horizontal. The constant acceleration value in the cable direction is 4 m/s². The water depth is measured as 1.5 m before the motion starts.  Determine the angle between the water surface and the horizontal.  Compute the maximum and minimum pressure values on the bottom of the tank.  How many volume of water are spilled?

Solutions

Expert Solution

Taking components of acceleration in horizontal and vertical directions- when taking an inertial frame of reference, accelerations will impose a load in the opposite direction. Thus in the vertical direction, effective gravitational acceleration will increase

g​​​​​eff = g+2 = 9.81+2 = 11.81 m/s²

And horizontal acceleration ax= 2√3 = 3.464 m/s²

(A) For constant linear acceleration case water forms linear surface inclined to horizontal such that its slope is in the ratio of Acceleration in horizontal and vertical direction i.e. if θ is the angle of the surface with horizontal, tanθ= ax/g​​​​​​eff = 3.464/11.81

Thus θ = 16.347°

(B) There are two cases possible in the final arrangement of the tank-

Case 1: bottom of tank visible

Case 2: bottom of the tank not visible

At the farther end of the tank, final depth will be 1.8 m. With the known slope of water, we can check whether the corresponding horizontal width is less or greater than the available width(4m).

tanθ= 1.8/required width

Thus required width= 1.8/tan(16.347°) = 6.13m > 4m so it is case 2 i.e. bottom of tank not visible. So the arrangement of the tank is as follows

Writing slope equation for inclined height of water, tanθ = y/4

Thus y= 4*tan(16.347°) = 1.173 m

So depth of water at nearer end say A is 1.8-y=0.627 m. Since depth is minimum at A, pressure at bottom will also be minimum.

Thus min pressure= ρ*g​​​​​​eff*h(A) = 1000*11.81*0.627 = 7.405 kPa

Also pressure at farther end say B will be max.

So max pressure = ρ*g​​​​​​eff*h(B)= 1000*11.81*1.8= 21.258 kPa

(C) Considering unit length of tank, volume spilled= initial volume of water - final volume of water

Initial volume = 1.5*4*1 =6 m³

Final volume = volume of trapezoid= ½*4*(1.8+0.627) = 4.854 m³

Thus volume of water spilled= 1.146 m³


Related Solutions

An 800-gallon, 1.2 m wide cylindrical water tank is filled to the brim. The tank has...
An 800-gallon, 1.2 m wide cylindrical water tank is filled to the brim. The tank has a hole formed at 13.3 cm above the ground. It is observed that water leaks out of the reservoir at a speed that reduces by 3.2 m.s-1 in 1 minute 39 seconds. If the tank was initially filled to the brim how much water leaked out of the tank, and 8.2 by how much shall the point, at which water lands, change? (1 gallon...
A conical tank of diameter 6 m and height 10 m is filled with water. Compute...
A conical tank of diameter 6 m and height 10 m is filled with water. Compute for the work needed to pump all the water 2 m above the tank. The water has a density of 1000 kg per cubic meter.
A rectangular tank 1.5 m wide, 3 m long and 1.8 m deep contains water to...
A rectangular tank 1.5 m wide, 3 m long and 1.8 m deep contains water to a depth of 1.2 m. Find the horizontal acceleration that may be imparted to the tank in the direction of its length so that 1. the water is just about to spill 2. the front bottom corner of the tank is just exposed. 3. the bottom of the tank is exposed to its midpoint. For (2) and (3) above, compute the volume of the...
Fluid Mechanics: A water tank is a cylinder 4 m in height and 2 meters in...
Fluid Mechanics: A water tank is a cylinder 4 m in height and 2 meters in diameter. The tank is full at time to. The tank sits on a platform 12 m tall. A water tap is located at the bottom center of the tank. The tap, when actuated, opens to a pipe 5 cm in radius. a.       Write down Bernoulli’s equation. Identify the Pressure, Kinetic and Potential Energy terms. Show that each has the units of an energy density...
A conical tank has height 9 m and radius 4 m at the base. Water flows...
A conical tank has height 9 m and radius 4 m at the base. Water flows at a rate of 3 m^3/min. How fast is the water level rising when the level is 1 m and 2 m? (Use symbolic notation and fractions where needed.) When the water level is 1 m, the water level is rising at a rate of _ .When the water level is 2 m, the water level is rising at a rate of _.
A large storage tank with an open top is filled to a height h0. The tank...
A large storage tank with an open top is filled to a height h0. The tank is punctured at a height h above the bottom of the tank. Find an expression for how far from the tank the exiting stream lands. (Let d be the horizontal distance the stream of water travels. Use any variable or symbol stated above as necessary. ? for the density of water and g. Do not substitute numerical values; use variables only.)
- A cylindrical tank is being filled simultaneously with water and sugar. The input of water...
- A cylindrical tank is being filled simultaneously with water and sugar. The input of water and sugar is carefully adjusted so that the concentration of sugar in the water is held constant at 5 grams per cubic meter. The tank has a radius of 5 meters and a height of 10 meters. At a particular point in time, the water level is 3 meters high and rising at a rate of .5 meters per second. At this time, how...
a) A full conical water tank has height 3 m and diameter across the top 2...
a) A full conical water tank has height 3 m and diameter across the top 2 m. It is leaking water at a rate of 10,000 cm^3 per minute. How fast is the height of the water decreasing when the volume of water is 3,000,000 cm^3 ? b) Two planes are approaching the same air traffic control tower at equal and constant altitude. Plane A is heading due north at 200 mph, while Plane B is heading due west at...
A closed, rigid tank is filled with water. Initially, the tank holds 0.6 lb of saturated...
A closed, rigid tank is filled with water. Initially, the tank holds 0.6 lb of saturated vapor and 6.0 lb of saturated liquid, each at 212°F. The water is heated until the tank contains only saturated vapor. Kinetic and potential energy effects can be ignored. Determine the volume of the tank, in ft3, the temperature at the final state, in °F, and the heat transfer, in Btu.
A tank whose bottom is a mirror is filled with water to a depth of 19.4...
A tank whose bottom is a mirror is filled with water to a depth of 19.4 . A small fish floats motionless 7.10 under the surface of the water. part A) What is the apparent depth of the fish when viewed at normal incidence to the water? Express your answer in centimeters. Use 1.33 for the index of refraction of water. Part B) What is the apparent depth of the reflection of the fish in the bottom of the tank...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT