Explanation Given: The gauge pressure of the water at C is P = 40 lb/in . 2 The velocity of water at A is v A = 12 ft/s . The velocity of water at B is v B = 25 ft/s . The diameter of the pipe at A and B is d A = d B = 0.5 in . The diameter of the pipe at C is d C = 0.75 in . . The density of water is ρ w = 62.4 lb/ft 3 . Draw the free body diagram of the elbow as shown in Figure 1. Write the formula for mass flow rate of the water. d m d t = ρ w Q (I) Here, ρ w is the density of the water and Q is the discharge. Write the relation between the discharge of water ( Q ) , area ( A ) and velocity ( v ) . Q = v A (II) v = Q A (III) Here, v is the velocity and A is the cross sectional area. Write formula for cross sectional area of the pipe. A = π d 2 4 (IV) Refer Figure (1). Write the steady flow equation of forces along x and y − a x e s . ∑ F x = d m B d t ( v B ) x + d m A d t ( v A ) x − d m C d t ( v C ) x (V) ∑ F y = d m B d t ( v B ) y + d m A d t ( v A ) y − d m C d t ( v C ) y (VI) Here, ∑ F x is the net forces along x − a x i s , ∑ F y is the net forces along y − a x i s . Here, d m d t is the rate of mass flow, v A is the velocity of the water at A , v B is the velocity of the water at B , v C is the velocity of the water at C , ∑ F x net forces along x − a x i s , ∑ F y net forces along y − a x i s and the suffixes x , y indicates the velocity of the water along x and y axes. Write the formula for the force exerted by the pressure ( P ) . F P = P A C (VII) Here, P is the pressure of the water and A C is the cross sectional area at C . Conclusion: Refer Equation (IV) Calculate the cross sectional area at C . A C = π d C 2 4 Substitute 0.75 in . for d C . A C = π ( 0.75 in . × 1 ft 12 in . ) 2 4 = 0.0009765 π Calculate the cross sectional area at A . A A = π d A 2 4 Substitute 0.5 in . for d A . A A = π ( 0.5 in . × 1 ft 12 in . ) 2 4 = 0.0004340 π Here, A A = A B = 0.0004340 π . Refer Equation (II) and (IV) Calculate the discharge of water at C . Q C = v C A C Substitute 0.0009765 π for A C . Q C = v C ( 0.0009765 π ) = v C ( 0.0009765 π ) ft 3 /s Calculate the discharge of water at A . Q A = v A A A Substitute 12 ft/s for v A and 0.0004340 π for A A . Q A = 12 ft/s ( 0.0004340 π ) = ( 0.0052083 π ) ft 3 /s Calculate the discharge of water at B . Q B = v B A B Substitute 25 ft/s for v B and 0.0004340 π for A B . Q B = 25 ft/s ( 0.0004340 π ) = ( 0.01085 π ) ft 3 /s Refer Figure (I). The flow of water is divided into two discharges at A and B . Hence the discharge of water at A is equal to the sum of the discharge of water at A and B . Q C = Q A + Q B Substitute v C ( 0.0009765 π ) ft 3 /s for Q C , ( 0.0052083 π ) ft 3 /s for Q A and ( 0.01085 π ) ft 3 /s for Q B . v C ( 0.0009765 π ) ft 3 /s = ( 0.0052083 π ) ft 3 /s + ( 0.01085 π ) ft 3 /s v C = 0.0160583 π 0.0009765 π v C = 16.4444 ft/s Refer Equation (I). Calculate the mass flow rate of water at A . d m A d t = ρ w Q A Substitute 62.4 lb/ft 3 for ρ w and ( 0.0052083 π ) ft 3 /s for Q A . d m A d t = ( 62.4 lb/ft 3 × 1 32.2 ft/s 2 ) [ ( 0

15th Edition

ISBN: 9780137514724

Author: HIBBELER

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 15, Problem 121P

To determine

The horizontal and vertical force components exerted on the elbow.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 15, Problem 120P

Chapter 15, Problem 122P

Students have asked these similar questions

: Water Flow into horizontal pipe with velocity of v. Determine the horizontal and vertical component of force and the moment at A need to hold the elbow in place. Neglected the weight of the elbow and the water within it . Take v between 1 to 5 m/s and D1 between 0.2 to 1.0 m and D2 between 1.0 to 0.2 m. 3 m D1 v1 A В

The winding drum D is drawing in the cable at an accelerated rate of 4.5 m/s^2. Determine the cable tension if the suspended crate has a mass of 1000 kg.

6-10. Water flows through the elbow with a velocity of 18 ft/s. Determine the horizontal and vertical components of force the support at C exerts on the elbow. The pressure within the pipe at A and B is 28 psi. The flow occurs in the horizontal plane. Assume there is no support at A and B. 18 ft/s 4 in. 4 in. 60 130

Chapter 15 Solutions

PEARSON ETEXT ENGINEERING MECH & STATS

Ch. 15 - The 0.5kg ball strikes the rough ground and...Ch. 15 - Prob. 2FP Ch. 15 - Prob. 3FP Ch. 15 - The wheels of the 1.5-Mg car generate the traction...Ch. 15 - Prob. 5FP Ch. 15 - If the coefficient of kinetic friction between the...Ch. 15 - Prob. 3P Ch. 15 - Each of the cables can sustain a maximum tension...Ch. 15 - Crates A and B weigh 100 lb and 50 lb,...Ch. 15 - Prob. 8P

Ch. 15 - Prob. 9P Ch. 15 - During operation the jack hammer strikes the...Ch. 15 - For a short period of time, the frictional driving...Ch. 15 - The 2.5-Mg van is traveling with a speed of 100...Ch. 15 - Prob. 14P Ch. 15 - The towing force acting on the 400-kg safe varies...Ch. 15 - Prob. 18P Ch. 15 - Prob. 19P Ch. 15 - If it takes 35 s for the 50-Mg tugboat to increase...Ch. 15 - Prob. 23P Ch. 15 - The balloon has a total mass of 400 kg including...Ch. 15 - Prob. 26P Ch. 15 - Prob. 30P Ch. 15 - Prob. 7FP Ch. 15 - The cart and package have a mass of 20 kg and 5...Ch. 15 - The 5-kg block A has an initial speed of 5 m/s as...Ch. 15 - Prob. 10FP Ch. 15 - Prob. 11FP Ch. 15 - The cannon and support without a projectile have a...Ch. 15 - The 5-Mg bus B is traveling to the right at 20...Ch. 15 - Prob. 36P Ch. 15 - A railroad car having a mass of 15 Mg is coasting...Ch. 15 - A ballistic pendulum consists of a 4-kg wooden...Ch. 15 - Prob. 39P Ch. 15 - Prob. 43P Ch. 15 - Prob. 44P Ch. 15 - Prob. 45P Ch. 15 - The 30-Mg freight car A and 15-Mg freight car B...Ch. 15 - Blocks A and B have masses of 40 kg and 60 kg,...Ch. 15 - Block A has a mass of 5 kg and is placed on the...Ch. 15 - Solve Prob. 15-53 if the coefficient of kinetic...Ch. 15 - Prob. 56P Ch. 15 - Prob. 13FP Ch. 15 - Prob. 14FP Ch. 15 - The 30-lb package A has a speed of 5 ft/s when it...Ch. 15 - The ball strikes the smooth wall with a velocity...Ch. 15 - Prob. 17FP Ch. 15 - Prob. 18FP Ch. 15 - Prob. 58P Ch. 15 - Prob. 59P Ch. 15 - Prob. 61P Ch. 15 - Prob. 62P Ch. 15 - Prob. 63P Ch. 15 - Prob. 64P Ch. 15 - A 1-lb ball A is traveling horizontally at 20 ft/s...Ch. 15 - Prob. 69P Ch. 15 - Prob. 73P Ch. 15 - Two smooth disks A and B each have a mass of 0.5...Ch. 15 - Prob. 75P Ch. 15 - The cue ball A is given an initial velocity (vA)1...Ch. 15 - Prob. 78P Ch. 15 - Prob. 79P Ch. 15 - A ball of negligible size and mass m is given a...Ch. 15 - Prob. 81P Ch. 15 - The 20-lb box slides on the surface for which k =...Ch. 15 - Prob. 84P Ch. 15 - Prob. 85P Ch. 15 - Prob. 90P Ch. 15 - Prob. 92P Ch. 15 - Disks A and B have a mass of 15 kg and 10 kg,...Ch. 15 - Prob. 19FP Ch. 15 - Prob. 20FP Ch. 15 - Initially the 5-kg block is moving with a constant...Ch. 15 - Prob. 22FP Ch. 15 - Prob. 23FP Ch. 15 - Prob. 24FP Ch. 15 - Determine the angular momentum HO of the 6-lb...Ch. 15 - Determine the angular momentum HP of the 6-lb...Ch. 15 - Prob. 96P Ch. 15 - Determine the angular momentum Hp, of each of the...Ch. 15 - Prob. 98P Ch. 15 - Determine the angular momentum Hp of the 3-kg...Ch. 15 - The 800-lb roller-coaster car starts from rest on...Ch. 15 - The 800-lb roller-coaster car starts from rest on...Ch. 15 - If the rod of negligible mass is subjected to a...Ch. 15 - The amusement park ride consists of a 200-kg car...Ch. 15 - An earth satellite of mass 700 kg is launched into...Ch. 15 - Prob. 115P Ch. 15 - Prob. 116P Ch. 15 - Prob. 119P Ch. 15 - The gauge pressure of water at A is 150.5 kPa....Ch. 15 - Prob. 121P Ch. 15 - The fountain shoots water in the direction shown....Ch. 15 - A plow located on the front of a locomotive scoops...Ch. 15 - Prob. 124P Ch. 15 - Water is discharged from a nozzle with a velocity...Ch. 15 - Prob. 127P Ch. 15 - Prob. 128P Ch. 15 - Sand drops onto the 2-Mg empty rail car at 50 kg/s...Ch. 15 - Prob. 133P Ch. 15 - A rocket has an empty weight of 500 lb and carries...Ch. 15 - Prob. 135P Ch. 15 - Prob. 138P Ch. 15 - The missile weighs 40 000 lb. The constant thrust...Ch. 15 - Prob. 140P Ch. 15 - Prob. 1RP Ch. 15 - Prob. 2RP Ch. 15 - Prob. 3RP Ch. 15 - Prob. 4RP Ch. 15 - The 200-g projectile is fired with a velocity of...Ch. 15 - Block A has a mass of 3 kg and is sliding on a...Ch. 15 - Two smooth billiard balls A and B have an equal...Ch. 15 - Prob. 8RP

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.

The horizontal and vertical force components exerted on the elbow.

Solution Summary: The author explains how to determine the horizontal and vertical force components exerted on the elbow.

Videos

The horizontal and vertical force components exerted on the elbow.

Want to see the full answer?

Chapter 15 Solutions