Water at 20°C (ρ=998 kg/m

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

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

= 10𝑐𝑚, while 𝐷

= 3𝑐𝑚. At a flow rate of 0.0153 m

/s, the pressure p

= 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 = ∫ 𝜌𝑉_{𝐶𝑆 𝑅}. 𝑛 𝑑𝐴 Momentum Equation:

∑ 𝐹 = ^𝑑

𝑑𝑡∫ 𝑉𝜌𝑑∀_𝐶𝑉 + ∫ 𝑉𝜌𝑉_{𝐶𝑆 𝑅}. 𝑛 𝑑𝐴

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

---

Solution:

a) Continuity:

Q = V

A

= V

A

𝑉

=

𝐴₁

=

(^𝜋₄)(0.1)²

= 1.95 𝑚/𝑠

𝑉

=

𝐴₂

=

(^𝜋₄)(0.03)²

= 21.64 𝑚/𝑠 x – Momentum:

∑ 𝐹

= 𝑚̇𝑢

− 𝑚̇𝑢

−𝐹

+ 𝑝

𝐴

= 𝜌𝑄(−𝑉

cos 40° − 𝑉

) 𝐹

= (233 × 10

)

4

(0.1)

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

(+1)

(+3) (+2)

(+1)

(+1) (+2)