Concept explainers
(a)
The force exerted by the water on the bottom.
(a)
Answer to Problem 8P
The force exerted by the water on the bottom is
Explanation of Solution
Write the equation for pressure on the bottom due to water.
Here,
Rewrite the above equation for
Write the equation for the pressure on the bottom due to water.
Here,
Conclusion:
Substitute
Substitute
Therefore, the force exerted by the water on the bottom is
(b)
The force exerted by the water on each end.
(b)
Answer to Problem 8P
The force exerted by the water on each end is
Explanation of Solution
Pressure varies with depth.
Write the equation for the force on a strip of height
Here,
Write the equation for
Write the equation for
Here,
Put the above two equations in equation (III).
Integrate the above equation over the entire height of the strip.
Write the equation for the total area.
The pressure at the top of the pool is zero.
Write the equation for the pressure at surface of the pool.
Here,
Write the equation for the average pressure.
Here,
Put equations (II) and (VI) in the above equation.
Put equations (V) and (VII) in equation (IV).
Put equation (II) in equation (VII).
Conclusion:
Substitute
The length of each end will be
Substitute
Substitute
The force will be directed outward.
Therefore, the force exerted by the water on each end is
(c)
The force exerted by the water on each side.
(c)
Answer to Problem 8P
The force exerted by the water on each side is
Explanation of Solution
Equation (VIII) gives the force exerted on each side of the swimming pool by water.
Conclusion:
The length of each side will be
Substitute
Substitute
The force will be directed outward.
Therefore, the force exerted by the water on each side is
Want to see more full solutions like this?
Chapter 15 Solutions
Principles of Physics: A Calculus-Based Text
- The gravitational force exerted on a solid object is 5.00 N. When the object is suspended from a spring scale and submerged in water, the scale reads 3.50 N (Fig. P15.24). Find the density of the object. Figure P15.24 Problems 24 and 25.arrow_forwardReview. The tank in Figure P15.13 is filled with water of depth d = 2.00 m. At the bottom of one sidewall is a rectangular hatch of height h = 1.00 m and width w = 2.00 m that is hinged at the top of the hatch. (a) Determine the magnitude of the force the water exerts on the hatch. (b) Find the magnitude of the torque exerted by the water about the hinges.arrow_forwardA 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 (Fig. P15.39). Find an expression for how far from the tank the exiting stream lands. Figure P15.39arrow_forward
- An incompressible, nonviscous fluid is initially at rest in the vertical portion of the pipe shown in Figure P15.61a, where L = 2.00 m. When the valve is opened, the fluid flows into the horizontal section of the pipe. What is the fluids speed when all the fluid is in the horizontal section as shown in Figure P15.61b? Assume the cross-sectional area of the entire pipe is constant. Figure P15.61arrow_forwardA horizontal pipe 10.0 cm in diameter has a smooth reduction to a pipe 5.00 cm in diameter. If the pressure of the water in the larger pipe is 8.00 104 Pa and the pressure in the smaller pipe is 6.00 104 Pa, at what rate does water flow through the pipes?arrow_forwardA 10.0-kg block of metal measuring 12.0 cm by 10.0 cm by 10.0 cm is suspended from a scale and immersed in water as shown in Figure P15.24b. The 12.0-cm dimension is vertical, and the top of the block is 5.00 cm below the surface of the water. (a) What are the magnitudes of the forces acting on the top and on the bottom of the block due to the surrounding water? (b) What is the reading of the spring scale? (c) Show that the buoyant force equals the difference between the forces at the top and bottom of the block.arrow_forward
- A 1.00-kg beaker containing 2.00 kg of oil (density = 916.0 kg/m3) rests on a scale. A 2.00-kg block of iron suspended from a spring scale is completely submerged in the oil as shown in Figure P15.63. Determine the equilibrium readings of both scales. Figure P15.63 Problems 63 and 64.arrow_forwardA U-tube open at both ends is partially filled with water (Fig. P15.67a). Oil having a density 750 kg/m3 is then poured into the right arm and forms a column L = 5.00 cm high (Fig. P15.67b). (a) Determine the difference h in the heights of the two liquid surfaces. (b) The right arm is then shielded from any air motion while air is blown across the top of the left arm until the surfaces of the two liquids are at the same height (Fig. P15.67c). Determine the speed of the air being blown across the left arm. Take the density of air as constant at 1.20 kg/m3.arrow_forwardA beaker of mass mb containing oil of mass mo and density o rests on a scale. A block of iron of mass mFe suspended from a spring scale is completely submerged in the oil as shown in Figure P15.63. Determine the equilibrium readings of both scales. Figure P15.63 Problems 63 and 64.arrow_forward
- Fluid originally flows through a tube at a rate of 100 cm3/s. To illustrate the sensitivity of flow rate to various factors, calculate be new flow rate for following changes with all other factors remaining the same as in original conditions. (a) Pressure difference increases by a factor of 1.50. (b) A new fluid wit 3.00 times greater viscosity is substituted. (c) The tube is replaced by one having 4.00 times the length. (d) Another tube used with a 0.100 times the original. (e) Yet another tube is substituted with a radius 0.100 times the original and half length, and pressure difference is increased by factor of 1.50.arrow_forwardMercury is poured into a U-tube as shown in Figure P15.17a. The left arm of the tube has cross-sectional area A1 of 10.0 cm2, and the right arm has a cross-sectional area A2 of 5.00 cm2. One hundred grams of water are then poured into the right arm as shown in Figure P15.17b. (a) Determine the length of the water column in the right arm of the U-tube. (b) Given that the density of mercury is 13.6 g/cm3, what distance h does the mercury rise in the left arm?arrow_forwardSuppose water is raised by capillary action to a height of 5.00 cm in a glass tube. (a) To what height will it be raised in a paraffin tube of the same radius? (b) In a silver tube of the same radius?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College