Name :_________________ Quiz: No. 4 Time: 15 minutes Student ID# : ____________ Course: ME 5160, Fall 2021
--- The exam is closed book and closed notes.
A jet of oil strikes the vertical plate as shown in below figure. A force F≈ 680N is required to hold the plate stationary. Consider the head loss of nozzle. (Use 𝐾
𝑐= 0.6), estimate (a) the mass flow rate of alcohol and (b) the absolute pressure at section 1.
[𝜌𝑜𝑖𝑙 = 0.81 × 998 = 808.38𝑘𝑔/𝑚3]
Name :_________________ Quiz: No. 4 Time: 15 minutes Student ID# : ____________ Course: ME 5160, Fall 2021
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Solution:
A momentum analysis of the plate will give
F = −𝑚̇𝑉
2= −𝜌𝐴
2𝑉
22𝐴
2= 𝜋 4 𝐷
22−F = 𝜌 𝜋 4 𝐷
22𝑉
22𝑉
22= −F 𝜌 𝜋
4 𝐷
22𝑉
2= √ −4𝐹
𝜌𝜋𝐷
22= √ 4 × 680
808.38 × 𝜋 × 0.035
2= 29.569m/s
Use continuity equation to get 𝑉
1𝐴
1𝑉
1= 𝐴
2𝑉
2𝑉
1= 𝐴
2𝑉
2𝐴
1= 0.035
20.130
2× 29.569 = 2.1433𝑚/𝑠
Mass flow rate: 𝜌𝐴
1𝑉
1= 808.38 × (
𝜋4
0.13
2) × 2.1433 = 22.997𝑘𝑔/𝑠 Calculate pressure difference using Bernoulli (Energy) equation
𝑝
1− 𝑝
2= 1
2 𝜌(𝑉
22− 𝑉
12) + 𝜌𝑔ℎ
𝑙𝑜𝑠𝑠𝑝
1− 𝑝
2= 1
2 𝜌(𝑉
22− 𝑉
12) + 𝜌𝑔𝐾
𝑐𝑉
222𝑔
𝑝
1− 𝑝
2=
12
(808.38)(29.569
2− 2.1433
2) + (808.38)(9.81) (0.6
29.56922×9.81
)
𝑝
1− 𝑝
2= 351536.9876 + 212036.2376 = 563573.2252 𝑃𝑎 ≈ 563.57𝑘𝑃𝑎
∴ 𝑝
1= 563.57 + 𝑝
2= 563.57 + 101 = 664.57 𝑘𝑃𝑎
(+3)
(+2)
(+1)
(+2) (+2)
