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laiz [17]
3 years ago
12

A pressure difference of 6.00 x 104 Pa is required to maintain a volume flow rate of 0.400 m3 /s for a viscous fluid flowing thr

ough a section of cylindrical pipe that has a radius 0.330 m. What pressure difference is required to maintain the same volume flow rate if the radius of the pipe is decreased to 0.110 m?
Physics
1 answer:
Olin [163]3 years ago
8 0

Answer:

(P₁ - P₂)f = 4.86*10⁶ Pa

Explanation:

To determine how variables affect the flow rate of an incompressible fluid undergoing laminate flow in a cylindrical tube, we use Poiseuille's equation.

Q = Πr⁴ / 8η * [(p₁ - p₂) / L]

Q = 0.40 m³/s

P₁ - P₂ = 6*10⁴ pa

r₁ = 0.33m

r₂ = 0.11m

According to Poiseuille's law, the pressure difference is inversely proportional to the radius of the pipe raised to power of 4.

P₁ - P₂ = 1 / r⁴

(P₁ - P₂)i / (P₁ - P₂)f = R⁴f / Ri⁴

Saving for (P₁ - P₂)f

(P₁ - P₂)f = (Rf⁴ / Ri⁴) * (P₁ - P₂)i

(P₁ - P₂)f = [(0.33)⁴ / (0.11)⁴] = 6*10⁴

(P₁ - P₂)f = 4.86*10⁶pa.

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An air gun fires 2 gram pellets at 60 m/s at a 45 gram golfball initially at rest. The pellets rebound at a speed 40 m/s and are
snow_lady [41]

Answer:

0.16 kgm/s

Explanation:

m_1 = Mass of pellet = 2 g

m_2 = Mass of golf ball = 45 g

u_1 = Initial Velocity of pellet  = 60 m/s

u_2 = Initial Velocity of golf ball = 0 m/s

v_1 = Final Velocity of pellet = 40 m/s

v_2 = Final Velocity of golf ball

In this system the linear momentum is conserved

m_1u_1+m_2u_2=m_1v_1+m_2v_2\\\Rightarrow m_2v_2=m_1u_1+m_2u_2-m_1v_1\\\Rightarrow m_2v_2=0.002\times 60+0-0.002\times 40\\\Rightarrow m_2v_2=0.04

As the golf ball is being shot 4 times every second the momentum delivered to the golf ball each second is 4\times 0.04=0.16\ kgm/s

8 0
3 years ago
A satellite is in a circular orbit around the Earth at an altitude of 3.18x10 m. Find the period and th orbital speed of the sat
Leona [35]

Answer:

112.17 m/s

56.427 years

Explanation:

h = 3.18 x 10^10 m

R = 6.4 x 10^6 m

r = R + h = 3.18064 x 10^10 m

M = 6 x 10^24 kg

The formula for the orbital velocity is given by

v = \sqrt{\frac{G M }{r}}

v = \sqrt{\frac{6.67 \times 10^{-11}\times 6\times 10^{24}  }{3.18064\times 10^{10}}}

v = 112.17 m/s

Orbital period, T = 2 x 3.14 x 3.18064 x 10^10 / 112.17

T = 0.178 x 10^10 s

T = 56.427 years

8 0
3 years ago
A piston-cylinder device initially contains 0.08 m3 of nitrogen gas at 150 kPa and 200°C. The nitrogen is now expanded to a pres
Lemur [1.5K]

Answer:

V_2 = 0.125 m^3

Work done =  = 5 kJ

Explanation:

Given data:

volume of nitrogen v_1 = 0.08 m^3

P_1 = 150 kPa

T_1 = 200 degree celcius = 473 Kelvin

P_2 = 80 kPa

Polytropic exponent n = 1.4

\frac{T_2}{T_1} = [\frac{P_2}{P_1}]^{\frac{n-1}{n}

putting all value

\frac{T_2}{473} = [\frac{80}{150}]^{\frac{1.4-1}{1.4}

\frac{T_2} = 395.23 K = 122.08 DEGREE \ CELCIUS

polytropic process is given as

P_1 V_1^n = P_2 V_2^n

150\times 0.08^{1.4} = 80 \times V_2^{1.4}

V_2 = 0.125 m^3

work done = \frac{P_1 V_1 -P_2 V_2}{n-1}

= \frac{150 \times 0.8 - 80 \times 0.125}{1.4-1}

                  = 5 kJ

4 0
3 years ago
What is Vatiable Velocity?​
Allushta [10]

Answer:

Explanation: When a body covers unequal distances in equal intervals of time in a specified direction, the body is said to be moving with a variable velocity. Example: A rotating fan at a constant speed has variable velocity, because of continuous change in direction.

7 0
2 years ago
A track star runs the first 500 meters of a race in only 75 seconds. What is the track
irina1246 [14]

Answer:

6.667 m/s

Explanation:

500 meters = 75 seconds

500 meters / 75 seconds = 6.667 m/s

7 0
3 years ago
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