Concept explainers
Review. The lank in Figure P14.15 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 in 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.
(a)
The amount of force water exerts on the hatch.
Answer to Problem 14.15P
The amount of force water exerts on the hatch is
Explanation of Solution
Given info: The depth of water in the tank is
Write the expression for the force exerted on the strip.
Here,
Write the expression for pressure exerted on the strip.
Here,
The area of the cross section of the strip is,
Here,
Substitute
As, the pressure varies with the depth so the force exerted is also vary.
Write the expression for force exerted on the rectangular height,
Here,
Substitute
The density of the water is
Substitute
Conclusion:
Therefore, the amount of force water exerts on the hatch is
(b)
The amount of the torque exerted by the water about the hinges.
Answer to Problem 14.15P
The amount of the torque exerted by the water about the hinges is
Explanation of Solution
Given info: The depth of water in the tank is
Write the expression for the torque about the hinge.
Here,
From part (a), the force exerted on the rectangular hatch is,
Substitute
Write the expression for the torque about the hinge,
Substitute
The density of the water is
Substitute
Conclusion:
Therefore, the amount of the torque exerted by the water about the hinges is
Want to see more full solutions like this?
Chapter 14 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
- Review. 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 fluid flows through a horizontal pipe that widens, making a 45 angle with the y axis (Fig. P15.48). The thin part of the pipe has radius R, and the fluids speed in the thin part of the pipe is v0. The origin of the coordinate system is at the point where the pipe begins to widen. The pipes cross section is circular. a. Find an expression for the speed v(x) of the fluid as a function of position for x 0 b. Plot your result: v(x) versus x. FIGURE P15.48 (a) The continuity equation (Eq. 15.21) relates the cross-sectional area to the speed of the fluid traveling through the pipe. A0v0 = A(x)v(x) v(x)=A0v0A(x) The cross sectional area is the area of a circle whose radius is y(x). The widening pan of the pipe is a straight line with slope of 1 and intercept y(0) = R. y(x) = mx + b = x + R A(x) = [y(x)]2 = (x + R)2 Plug this into the formula for the velocity. Plug this into the formula for the velocity. v(x)=A0v0(x+R)2arrow_forwardThe small piston of a hydraulic lift (Fig. P14.8) has a cross-sectional area of 3.00 cm2, and its large piston has a cross-sectional area of 200 cm2. What downward force of magnitude F1 must be applied to the small piston for the lift to raise a load whose weight is Fg = 15.0 kN?arrow_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_forwardThe small piston of a hydraulic lift (Fig. P15.6) has a cross-sectional area of 3.00 cm2, and its large piston has a cross-sectional area of 200 cm2. What downward force of magnitude F1 must be applied to the small piston for the lift to raise a load whose weight is Fg = 15.0 kN? Figure P15.6arrow_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
- Mercury 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_forwardA uniform wooden board of length L and mass M is hinged at the top of a vertical wall of a container partially filled with a certain liquid (Fig. P15.81). (If there were no liquid in the container, the board would hang straight down.) Three-fifths of the length of the board is submerged in the liquid when the board is in equilibrium. Find the ratio of the densities of the liquid and the board.arrow_forwardThe inside diameters of the larger portions of the horizontal pipe depicted in Figure P9.45 are 2.50 era. Water flows to the right at a rate of 1.80 104 m3/s. Determine the inside diameter of the constriction. Figure P9.45arrow_forward
- Figure P15.47 shows a stream of water in steady flow from a kitchen faucet. At the faucet, the diameter of the stream is 0.960 cm. The stream fills a 125-cm3 container in 16.3 s. Find the diameter of the stream 13.0 cm below the opening of the faucet. Figure P15.47arrow_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_forwardReview. The tank in Figure P15.13 is filled with water of depth d. At the bottom of one sidewall is a rectangular hatch of height h and width w 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 die water about die hinges.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning