Explanation Given: The water is discharge at an angle of 30 ° to the horizontal. The cross sectional area of the water stream is 2 in 2 . The density of water is ρ w = 62.4 lb/ft 3 . Draw the free body diagram of the water stream as shown in Figure 1. Refer Figure (1). Write the formula for position of the water stream along x − a x i s . s x = ( s 0 ) x + v o t (I) Here, s is the final position, s 0 is the initial position, v 0 is the initial velocity, and t is the time. Write the formula for velocity of the water stream along y − a x i s . v y = ( v 0 ) y + g t (II) Here, v is the final velocity, v 0 is the initial velocity, g is the acceleration due to gravity. Write the formula for mass flow rate of the water. d m d t = ρ w A v (III) Here, ρ w is the density of the water, A is cross sectional area and v is the velocity. Refer Figure (1). Write the steady flow equation of forces along x − a x i s . ∑ F x = d m d t [ ( v 2 ) x − ( v 1 ) x ] (IV) Here, d m d t is the rate of mass flow, v 1 is the initial velocity of the water stream at B , v 2 is the final velocity of the water stream at B and ∑ F x is the net forces along x − a x i s . Conclusion: Refer Figure (1a). The initial velocity of the water stream along x − a x i s is v 0 = v A cos 30 ° When, the final position of the water stream is s = 20 ft and the initial position is ( s 0 ) x = 0 . Substitute 20 ft for s x , 0 for ( s 0 ) x and v A cos 30 ° in Equation (I). 20 ft = 0 + ( v A cos 30 ° ) t ( 0.866 v A ) t = 20 0.866 v A t = 20 (V) Refer Figure (1a). The initial velocity ( v 0 ) of the water stream at A and the final velocity ( v ) of the water stream at B is equal in magnitude and opposite in their directions. v = v 0 = v A = v B The initial velocity of the water stream along y − a x i s is at A . v 0 = v A = v A sin 30 ° The final velocity of the water stream along y − a x i s is at B . v = v B = − v A sin 30 ° Substitute − v A sin 30 ° for v y , v A sin 30 ° for ( v 0 ) y and 32

Engineering Mechanics: Dynamics (14th Edition)

14th Edition

ISBN: 9780133915389

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 15.9, Problem 122P

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Chapter 15.9, Problem 121P

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Engineering Mechanics: Dynamics (14th Edition)

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The force exerted by the water stream on the concrete wall at B .

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