A square aquarium, 5 meters long and 3 meters deep is full of water. Use the fact that the density of water is 1000 kg m3 and acceleration due to gravity is g = 9.8 m sec2. Determine the following. a. The hydrostatic pressure on the bottom of the aquarium is Pascal b. The hydrostatic force on the bottom of the aquarium is Newtons c. The hydrostatic force on one side of the aquarium is Newtons
A large aquarium has the triangluar viewing window shown below. The vertices are at (−16, 0) and (16, 0) and (0, 8). The water surface is at y = 21 (shown by the blue line). All distances are in feet. The weight density of water is 62.5 lbs/ft∧3. Find the hydrostatic force on the window. (graph not to scale) lbs
A vertical dam on a large lake is 30 ft tall and 60 ft wide, and the water level is 3 ft below the top of the dam. In the middle of the dam at the very bottom is a gate the shape of an equilateral triangle 12 ft on a side as shown in the figure below. (Assume a density of water ρ = 62.4 lb/ft3.) Find the hydrostatic force (in lb) on the gate. (Round your answer to the nearest integer.) Ib
A trough whose cross section is an equilateral triangle with side a = 4 m long is filled with water. What is the force due to water pressure on one end of the trough? (Hint: Using SI units, ρg = 9800 kg/(m⋅s2).) (Express numbers in exact form. Use symbolic notation and fractions where needed.)
Hydrostatic Force: A vertical semi-circular plate is partially submerged in water as shown in the figure below, where the given dimensions are in feet. Recall that water has a weight density of 62.5 pounds per cubic foot. Set up but do not evaluate or even algebraically simplify an integral that represents the total hydrostatic force on the plate. ** Set up but do NOT evaluate**
[PHYSICS AND ENGINEERING] Hydrostatic Force. A vertical semicircular plate is in the wall of a swimming pool. The top of the plate is 4 feet below the water level. The radius of the semicircle is 3 feet. Recall that water has a weight density of 62.5 pounds per cubic foot. Set up but DO NOT EVALUATE or even algebraically simplify an integral that represents the total hydrostatic force on the plate.
What is the orientation of the hydrostratic force on a planar surface? How does the orientation and magnitude of the hydrostatic force change if the submerged surface is rotated 90∘ about its centroid? Consider the submerged body below. Sketch the pressure distribution around the entire surface of the body.
A semicircular plate with radius 4 m is submerged vertically in water so that the top is 2 m above the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the mass density of water is 1000 kg/m3.) 2ρg∫ 2 ◻ )dx ≈ ◻ N
A vertical dam retains 18 m of water. It is pierced at its base with a semi-circular door 4 m in diameter (the base of the door is its diameter), as indicated in the figure below. a) Let y denote the height in meters measured from the base of the dam. The hydrostatic force exerted by the water on the portion of the door comprised between y m and y + Δy m is approximately p(y) Δy N. What is p(y)? Note that the density of water is ρ = 1000 Kg/m3 and the acceleration due to gravity on the Earth's surface is g = 9.8 m/s2. Express your answer as a formula. Answer: b) In Newtons, what is the total hydrostatic force exerted on the door? FORMATTING: If you round your answer, ensure that the round-off error is less than 1 % of the value. Answer:
A vertical plate is submerged in water and has the indicated shape. (i) Express the hydrostatic force (in N) against one side of the plate as an integral (let the positive direction be downwards) and evaluate it. (Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1,000 kg/m3.) ρg∫ 0 9 ( ◻ )dx ≈ ◻ N
A semicircular cover (shown in darker blue) is at the bottom of a vertical wall of a rectangular tank. Its radius is 0.43 m. You may assume that the flat side at the top is horizontal. The tank is partially filled with a liquid whose mass density is 826 kg/m3. For the following, round your answers to at least 3 significant figures and include the units. You may assume that the acceleration due to gravity is 9.81 m/s2. a. Find the hydrostatic force acting on the semicircular cover if the liquid is 0.43 m deep (i.e. the same as the height of the cover). Force = Find the depth of the liquid if the hydrostatic force acting on the cover is 1693 N. Depth = Find the depth of the liquid if the hydrostatic force acting on the cover is 144 N. Depth = Feel free to use a computer to solve this problem.
A vertical dam has a semicircular gate as shown in the figure. The total depth d of the figure is 10 m, the height h of air above the water level is 2 m, and the width w of the gate is 8 m. Set up an integral that can be used to find the hydrostatic force (in N) against the gate. (Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1,000 kg/m3.) ∫ 0 ( 1,000)(9.8) ( ) d x Find the hydrostatic force (in N ) against the gate. (Round your answer to the nearest whole number.) N
Find the hydrostatic force on the following triangular plate by a) constructing and evaluating the integral and b) the hydrostatic force equation. (For metric, take δ = ρg, ρ = 1000 kg/m3, g = 9.8 m/s2. For English take δ = 62.5 lbs ft3. 2 pts.
A semicircular plate with radius 7 m is submerged vertically in water so that the top is 3 m above the surface. (i) Express the hydrostatic force (in N ) against one side of the plate as an integral (let the positive direction be downwards) and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1,000 kg/m3.) 2ρg∫ 3 ◻⋅(◻)dx ≈ ◻ N
Consider the trough shown below. The ends of the trough are trapezoids with dimensions a = 1.4 m, b = 0.6 m and H = 0.9 m. The length of the trough is L = 3.5 m. The trough is filled with water to a depth of 0.5 m. For the following, round your answers to at least 3 significant figures and include the units. You may assume that the mass density of water is 1000 kg/m3 and the acceleration due to gravity is 9.81 m/s2 a. Find the volume of water in the trough. Volume of water = b. Find the hydrostatic force acting on each of the following sides of the trough. Force on the horizontal bottom surface = Force on the long vertical side = Force on each trapezoidal end = c. Find the height of the centre of pressure on the long vertical side of the trough. The centre of pressure is above the bottom of the trough. d. Find the centre of pressure on each trapezoidal end. The centre of pressure on each trapezoidal end is from the vertical side and above the bottom of the trough. Feel free to use a calculator or a computer to evaluate the integrals.
A circular plate with radius 7 m is submerged vertically in water as shown. Express the hydrostatic force (in N) against one side of the plate as an integral (let the positive direction be upwards) and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1,000 kg/m3.)
Evaluate the hydrostatic force one side of the plate when a vertical plate is submerged in water and has the following shape. Write your EXACT answer in terms of gρ or δ .
Find the hydrostatic force experienced by the vertically submerged plate. The dashed line segment indicates the water level. (a) A plate whose shape is a half disk of radius 2 meters is vertically submerged in water. Find the hydrostatic force experienced by the plate. (b) A plate whose shape is an equilateral triangle whose side length is 2 m is vertically submerged in water partially. The coordinate system is already set up for you. Find the hydrostatic force experienced by the plate.
A semi-circular vertical plate is partially submerged in the water as shown in the figure. What is the force on the plate due to hydrostatic pressure if the water level is 1 meter from the top of the plate. Set up the integral only. a. F = ρ g ∫ − 3 0 2 9 − y 2 ( y + 1 ) d y b. F = ρ g ∫ − 3 − 1 2 9 − y 2 ( y − 1 ) d y c. F = ρ g ∫ − 3 1 2 9 − y 2 ( y + 1 ) d y d. F = ρ g ∫ − 3 0 2 9 − y 2 ( y − 1 ) d y A semi-circular vertical plate is partially submerged in the water as shown in the figure. What is the force on the plate due to hydrostatic pressure if the water level is 1 meter from the top of the plate. Set up the integral only. a. None of the choices. b. 4.8 × 10 4 N c. 7.8 × 10 6 N d. 5.4 × 10 6 N e. 6.7 × 10 4 N
Find the hydrostatic force on a submerged vertical square plate of side s = 2 meters having its top side sitting at a height of h = 2 meters below the surface of the water. Use ρ = density of water and g = force due to gravity. Calculating this integral, your final answer is of the form kρg. What is the value of the constant k in your answer?
A vertical plate is submerged in water and has the indicated shape. Find the hydrostatic force against one side of the plate. Round your answer to the nearest whole number.
A plate whose shape is half disk of radius 8 meters is vertically submerged in water. The top of the plate is 2 m below the water level. (The dashed line segment indicates the water level.) Use ρ = 1000 kg/m3 and g = 9.8 m/s2. (a) Set up an appropriate coordinate system, draw the strip on the plate and determine its area Ak. (b) Determine the pressure Pk and force Fk experienced by the strip. (c) Set up an integral that represents the hydrostatic force experienced by the plate. The integral must contain all the details. Do not evaluate the integral.