Ensc 388 Assignment #1 (Basic Concepts)

ENSC 388

Assignment #1 (Basic Concepts)

Assignment date: Wednesday Sept. 16, 2009

Due date: Wednesday Sept. 23, 2009

Problem 1: (Static Pressure)

Both a gage and a manometer are attached to a gas tank to measure its pressure. If the reading on the pressure gage is 80 kPa, determine the distance between the two fluid levels of the manometer if the fluid is (a) mercury (ρ =13,600 kg/m³) or (b) water (ρ =1000 kg/m³).

P_g=80 kPa

h=?

GAS


Problem 2: (Buoyancy)

Balloons are often filled with helium gas because it weighs only about one-seventh of what air weighs under identical conditions. The buoyancy force which can be expressed as F_B = ρ_airgV_balloon will push the balloon upward. If the balloon has diameter of 10 m and carries two people, 70 kg each, determine (a) the acceleration of the balloon when it is first released and (b) the maximum amount of load, in kg, the balloon can carry. Assume the density of air is ρ =1.16 kg/m³, and neglect the weight of the ropes and the cage. (Answers: 16.5 m/s², 520.6 kg)

HELIUM

D=10 m

ρ=ρ_air/7


m=140 kg


Problem 3: (Hydrostatic pressure)

WATER

ρ =1000 kg/m³

OIL

ρ_s=0.85

h=10 m

The lower half of a 10-m-high cylindrical container is filled with water (ρ =1000 kg/m³) and the upper half with oil that has a specific gravity of 0.85. Determine the pressure difference between the top and bottom of the cylinder. (Answer: 90.7 kPa)


Patm

2

GAS

P_g=80kPa

h=?

Problem 1:

Find h if:

1. 
   Fluid is mercury (ρ_Hg=13,600 kg/m³)
   
2. 
   Fluid is mercury (ρ_H2O=1000 kg/m³)
   

1


- Assumption:

The pressure is uniform in the tank, thus we can determine the pressure at the gage port.

- Analysis

Starting with (gas pressure) and moving along the tube from point (1) by adding (as we go down) or subtracting (as we go up), the ρgh term(s) until we reach point (2), therefore;

Since tube at point (2) is open to atmosphere, .

P_gage (What we read on the pressure gage)

80 kPa =ρgh



m_he

F_B

D


Problem 2:

D=10 m

ρ_He= ρ_air/7 and ρ_air =1.16 kg/m³



a
m_people=140 kg


m_people
Assumption:


W
The wight of the ropes and cage is neglected.

(Free body diagram)

Analysis:

Starting with free body diagram. We also know that te buoyancy force is:

Newton law:

Therefore:

(1)

So,

(2)

Substituting values in Eq. (2),

The maximum amount of load that the balloon can carry can be calculated from;

Using Eq. (1),

This mass is including the mass of helium gas in the balloon. To calculate maximum load, mass of helium must subtracted from the maximum mass so,

1
Problem 3:


OIL

h=5 m

h=5 m


Analysis:


WATER

2
Starting with point (1) and adding terms gh as

we go down,

Substituting values,

Notes (1): Always substitute the numerical value at the last step.

Note (2): Write all the dimensions in your solution; check both sides of relationships for unit and dimension homogeneity.

M. Bahrami ENSC 388 Assignment # 1