Answer:
1. p = <u>14.63</u> lb/in² or <u>100890.608</u> Pa
2. p = <u>74676</u> Pa or <u>10.83</u> lb/in²
3. P = <u>2450</u> W or <u>3.28 </u>hp
4. = <u>490105</u> N/m²
Explanation:
1. Let's begin by listing out the given parameters:
density of mercury = 13.546 g/cm³ = 13546 kg/m³,
height of column = 76 cm = 0.76 m, acceleration due to gravity = 9.8m/s²
Using Pressure = density * acceleration due to gravity * height of column
p = ρ g h = 13546 * 9.8 * 0.76
p = <u>100890.608</u> Pa
To get the answer in lb/in², divide by 6895
p = 100890.608 ÷ 6895 = 14.632
p = <u>14.63</u> lb/in²
2. Let's list out the parameters given:
density of water = 62.43 lbm/ft³ = 62.43 * 16.018 = 1000kg/m³,
height of column = 25 ft = 25 ÷ 3.281 = 7.62 m,
acceleration due to gravity = 9.8m/s²
Using Pressure = density * acceleration due to gravity * height of column
p = ρ g h = 1000 * 9.8 * 7.62
p = <u>74676</u> Pa
To convert from Pa to lb/in², divide by 6895
p = 74676 ÷ 6895
p = <u>10.83</u> lb/in²
3. Let's list out the parameters given:
mass flow rate (ṁ) = 10 kg/s, = 5 m, = 30 m, Δh = 30 - 5 = 25 m, g = 9.8 m/s²
Using Power = Energy (Potential Energy) ÷ Time
Energy (Potential Energy) = m g h
Power = mgΔh ÷ t; m÷ t = ṁ
Substitute ṁ into the equation
P = ṁ g h = 10 * 9.8 * 25
P = <u>2450</u> W
To convert from W to hp, divide by 746
P = 2450 ÷ 746 = 3.284
P = <u>3.28 </u>hp
4. Let's list out the parameters given:
height (Δh) = 50 m, ṁ = 1 kg/s, g = 9.8 m/s²,
p2 = 105N/m², ρ = 1000 kg/m³
Using Bernoulli's Equation,
p1 + ½ρ()² + ρgh1 = p2 + ½ρ()² + ρgh2
Assuming steady state flow; = ⇒ - = 0
- = ½ρ( - )² + ρg( - )
- = ρgΔh
- 105 = 1000 * 9.8 * 50
= 490000 + 105 = 490105
= <u>490105</u> N/m²