Answer to Question #139252 in Mechanical Engineering for Yashwanth Kumar Reddy

Question #139252
A 30 cm diameter pipe carries water under a head of 20 meters with a velocity of 3.5
m/s. If the axis of the pipe turns through 450
, find the magnitude and direction force
on the bend.
1
Expert's answer
2020-10-20T14:12:41-0400

Given, diameter of pipe=30 cm,Head =20 m and velocity of flowing is 3.5 m/s

Axis of pipe turn by 45o now

Area of pipe flow ="\\frac{\\pi}{4}d^2=\\frac{3.14}{4}\\times (0.3)^2=0.07065 \\frac{m^3}{s}"

Now pressure with which fluid flowing is

"P_1= \\rho gH=1000\\times 9.8\\times 20=196000 N"

Now,

According to question force along x-axis will be


"F_x=\\rho Q(v_{1x}-v_{2x})+P_1A_{1x}+P_2A_{2x}"


"F_x=1000\\times (0.07065\\times 3.5)(3.5--3.5 cos 45)+196000\\times 0.07065+196000\\times 0.07065 \\times 0.707"

Fx=4310 N


Similarly we will get force in y-direction as

"F_y=\\rho Q(v_{1y}-v_{2y})+P_1A_{1y}+P_2A_{2y}"

"F_y=1000\\times (0.07065\\times 3.5)(3.5--3.5 cos 45)+196000\\times 0.07065+196000\\times 0.07065 \\times 0.707"

Fy= 23890 N

Net resultant force

"F=\\sqrt{ (F_x^2)+(F_y^2)}" = 24275 N

and the direction of force


"\\theta= tan^{-1} \\frac{F_y}{F_x}=79.77 ^o"


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Comments

Assignment Expert
23.12.20, 11:38

Dear Janet, Questions in this section are answered for free. We can't fulfill them all and there is no guarantee of answering certain question but we are doing our best. And if answer is published it means it was attentively checked by experts. You can try it yourself by publishing your question. Although if you have serious assignment that requires large amount of work and hence cannot be done for free you can submit it as assignment and our experts will surely assist you.

Janet
30.11.20, 08:18

how to get 0.707

Janet
30.11.20, 08:13

A water jet with a diameter of 70 mm is deflected by 60⁰ at the velocity of 36 m/s at the beginning of the blade as shown in figure below. Calculate the magnitude of the force generated by water on the blade when the velocity of water jet leaving the blade is 30 m/s due to friction.

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