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Water at 20°C (ρ=998 kg/m

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(1)

Name :_________________ Quiz: No. 3 Time: 15 minutes Student ID# : ____________ Course: ME 5160, Fall 2021

--- The exam is closed book and closed notes.

Water at 20°C (ρ=998 kg/m

3

) flows through the elbow and waterjet exits to the atmosphere. The diameter of pipe is 𝐷

1

= 10𝑐𝑚, while 𝐷

2

= 3𝑐𝑚. At a flow rate of 0.0153 m

3

/s, the pressure p

1

= 2.3atm (gage). Neglecting the weight of water and elbow, estimate x component of the force on the flange bolts at section 1.

{2.3atm = 233kPa}

Continuity Equation:

− 𝑑

𝑑𝑡∫ 𝜌𝑑∀𝐶𝑉 = ∫ 𝜌𝑉𝐶𝑆 𝑅. 𝑛 𝑑𝐴 Momentum Equation:

∑ 𝐹 = 𝑑

𝑑𝑡∫ 𝑉𝜌𝑑∀𝐶𝑉 + ∫ 𝑉𝜌𝑉𝐶𝑆 𝑅. 𝑛 𝑑𝐴

(2)

Name :_________________ Quiz: No. 3 Time: 15 minutes Student ID# : ____________ Course: ME 5160, Fall 2021

---

Solution:

a) Continuity:

Q = V

1

A

1

= V

2

A

2

𝑉

1

=

𝑄

𝐴1

=

0.0153

(𝜋4)(0.1)2

= 1.95 𝑚/𝑠

𝑉

2

=

𝑄

𝐴2

=

0.0153

(𝜋4)(0.03)2

= 21.64 𝑚/𝑠 x – Momentum:

∑ 𝐹

𝑥

= 𝑚̇𝑢

2

− 𝑚̇𝑢

1

−𝐹

𝑥,𝑏𝑜𝑙𝑡𝑠

+ 𝑝

1

𝐴

1

= 𝜌𝑄(−𝑉

2

cos 40° − 𝑉

1

) 𝐹

𝑥,𝑏𝑜𝑙𝑡𝑠

= (233 × 10

3

)

𝜋

4

(0.1)

2

+ (998)(0.0153)(21.64 cos 40° + 1.95) = 2113 𝑁

(+1)

(+3) (+2)

(+1)

(+1) (+2)

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