Explanation Given information: The angle between the two straight section of the rotating arm as θ = 120 ° . The rate of discharge ( Q ) of water through the sprinkler is 20 L/min . The velocity ( v ) of the rotating arm is 18 m/s . The magnitude of the friction couple ( M F ) is 0.375 N ⋅ m . Calculation: Calculate the mass flow rate ( Δ m Δ t ) of the water using the relation: d m d t = ρ Q (1) Here, ρ is the density of the water. Consider the density of the water is 1 , 000 kg/m 3 . Substitute 1 , 000 kg/m 3 for ρ and 20 L/min for Q in Equation (1). Δ m Δ t = 1 , 000 kg/m 3 × ( 20 L/min × 1 m 3 1 , 000 L × 1 min 60 s ) = 1 , 000 kg/m 3 × ( 20 L/min × 1 m 3 1 , 000 L × 1 min 60 s ) = 0.33333 kg/s Show the geometry of the arm of the sprinkler as shown in Figure 1. Refer Figure 1. The centre of the four rotating arm of the sprinkler is denoted by O . Refer the triangle Δ A B O . Apply the cosine law follows: ( O A ) 2 = ( O B ) 2 + ( B A ) 2 − 2 ( O B ) ( B A ) cos θ = 150 2 + 100 2 − 2 × 150 × 100 cos ( 120 ° ) = 150 2 + 100 2 − 2 × 150 × 100 × ( − 0.5 ) = 32 , 500 + 15 , 000 O A = 47 , 500 = 217.95 mm Apply the sine rule as follows: sin β A B = sin θ O A sin β 100 = sin ( 120 ) 217.95 sin β = ( 0.866 217.95 ) × 100 β = sin − 1 ( 0.39733 ) β = sin − 1 ( 0.39733 ) ≈ 23.411 ° Calculate the value of the angle β as follows: α = 180 ° − 120 ° − β = 60 ° − 23

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Fire safety

Fire safety is a new domain emerged in the early 90s to enable the design of buildings, structures, and infrastructure against destruction through fire. It also includes the provisions of building codes. This field is mostly associated with the design an…

Videos

Question

Chapter 14, Problem 14.115RP

To determine

Find the rate of rotation of the garden sprinkler.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14, Problem 14.114RP

Chapter 14, Problem 14.116RP

Students have asked these similar questions

Prior to takeoff, the pilot of a 3000-kg twin-engine airplane tests the reversible-pitch propellers by increasing the reverse thrust with the brakes at point B locked. Knowing that point G is the center of gravity of the airplane, determine the velocity of the air in the two 2.2-m-diameter slipstreams when the nose wheel A begins to lift off the ground. Assume P = 1.21 kg/m3 and neglect the approach velocity of the air.

A pump draws water from a reservoir A and lifts it to reservoir B. The loss of head from A to point 1 is 3 times the velocity head in the 150 mm pipe and the loss of head from point 2 to B is 25 times the velocity head in the 100 mm pipe. When reservoir A is a starting point at elevation 0 and connected to point 1, where point 1 is also connected with a pump and point 2 is at elevation 20 m. which is connected with a pump that travels to reservoir B at elevation of 240 m. The discharge is 25 liters/sec, compute the pressure head at point 1. a. 268 m b. 134 m c. 19.74 m d. 39.48 m

A 3140-lb car travels up the 4-percent incline shown. The car is subjected to a 70-lb aerodynamic drag force and a 51-lb force due to all other factors such as rolling resistance. Determine the power output required at a speed of 66 mi/hr if (a) the speed is constant and (b) the speed is increasing at the rate of 0.06g. Answers: (a) Constant speed: 100 v=66 mi/hr P= (b) Increase in speed is 0.06g: P = hp hp

Chapter 14 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 14.1 - A 30-g bullet is fired with a horizontal velocity...Ch. 14.1 - Two identical 1350-kg automobiles A and B are at...Ch. 14.1 - Prob. 14.3P Ch. 14.1 - Prob. 14.4P Ch. 14.1 - Two swimmers A and B, of weight 190 lb and 125 lb,...Ch. 14.1 - A 180-lb man and a 120-lb woman stand side by side...Ch. 14.1 - A 40-Mg boxcar A is moving in a railroad...Ch. 14.1 - Two identical cars A and B are at rest on a...Ch. 14.1 - A 20-kg base satellite deploys three...Ch. 14.1 - For the satellite system of Prob. 14.9, assuming...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Find the rate of rotation of the garden sprinkler.

Solution Summary: The author calculates the rate of rotation of the garden sprinkler using the relation: rho and 20

Concept explainers

Videos

Find the rate of rotation of the garden sprinkler.

Want to see the full answer?

Chapter 14 Solutions