The amount of fluid that moves past a point in area A per unit of time is known as the flow rate.
<h3>How do you find average velocity from flow rate?</h3>
- The amount of fluid that moves past a point in area A per unit of time is known as the flow rate. Here, a uniform pipe carrying the shaded fluid cylinder passes point P in time t. The cylinder's capacity is Ad, its average velocity is v=d/t, and its flow rate is Q=Ad/t=Av.
- The average fluid velocity for laminar flow through a pipe is equal to half of the fluid's greatest velocity at the pipe's center. The Hagen-Poiseuille equation is shown above. Since there is no acceleration in a steady and uniform flow, there is no force acting in the direction of the flow.
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The lifetime of a star is determined by its mass. The larger it’s mass, the shorter it’s lifetime
Answer:
a) The temperature is 48.41 K
b) P₁/P₀ = 1
c) PL/P₀ = 1
Explanation:
a) Given:
P₁/P₀ = 1/2
According the expression:
![\frac{P_{1} }{P_{o} } =\frac{e^{-\beta E_{1} } }{e^{-\beta E_{o} } } \\\frac{P_{1} }{P_{o} }=\frac{e^{-\beta E_{1} } }{e^{-\beta *0 } }\\\frac{P_{1} }{P_{o} }=e^{-\beta E} \\\beta =\frac{1}{kt} \\\frac{P_{1} }{P_{o} }=e^-{\frac{\epsilon }{kt} }](https://tex.z-dn.net/?f=%5Cfrac%7BP_%7B1%7D%20%7D%7BP_%7Bo%7D%20%7D%20%3D%5Cfrac%7Be%5E%7B-%5Cbeta%20E_%7B1%7D%20%7D%20%7D%7Be%5E%7B-%5Cbeta%20E_%7Bo%7D%20%7D%20%7D%20%5C%5C%5Cfrac%7BP_%7B1%7D%20%7D%7BP_%7Bo%7D%20%7D%3D%5Cfrac%7Be%5E%7B-%5Cbeta%20E_%7B1%7D%20%7D%20%7D%7Be%5E%7B-%5Cbeta%20%2A0%20%7D%20%7D%5C%5C%5Cfrac%7BP_%7B1%7D%20%7D%7BP_%7Bo%7D%20%7D%3De%5E%7B-%5Cbeta%20E%7D%20%5C%5C%5Cbeta%20%3D%5Cfrac%7B1%7D%7Bkt%7D%20%5C%5C%5Cfrac%7BP_%7B1%7D%20%7D%7BP_%7Bo%7D%20%7D%3De%5E-%7B%5Cfrac%7B%5Cepsilon%20%7D%7Bkt%7D%20%7D)
![\epsilon =hf=6.626x10^{-34} *2.1x10^{12} =1.39x10^{-21} J](https://tex.z-dn.net/?f=%5Cepsilon%20%3Dhf%3D6.626x10%5E%7B-34%7D%20%2A2.1x10%5E%7B12%7D%20%3D1.39x10%5E%7B-21%7D%20J)
k = Boltzmann constant = 1.38x10⁻²³
![\frac{1}{2} =e^{\frac{-4.63x10^{-22} }{1.38x10^{-23} T} } \\\frac{1}{2}=e^{33.55T} \\ln(1/2)=-33.55/T\\-0.693=-33.55/T\\T=48.41K](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%3De%5E%7B%5Cfrac%7B-4.63x10%5E%7B-22%7D%20%7D%7B1.38x10%5E%7B-23%7D%20T%7D%20%7D%20%5C%5C%5Cfrac%7B1%7D%7B2%7D%3De%5E%7B33.55T%7D%20%5C%5Cln%281%2F2%29%3D-33.55%2FT%5C%5C-0.693%3D-33.55%2FT%5C%5CT%3D48.41K)
b) If T = 10%
![T_{2} =0.1*48.41 =4.841K](https://tex.z-dn.net/?f=T_%7B2%7D%20%3D0.1%2A48.41%20%3D4.841K)
![\frac{P_{1} }{P_{o} } =e^{\frac{-4.63x10^{-22} }{1.38x10^{-23} *4.841} }=1](https://tex.z-dn.net/?f=%5Cfrac%7BP_%7B1%7D%20%7D%7BP_%7Bo%7D%20%7D%20%3De%5E%7B%5Cfrac%7B-4.63x10%5E%7B-22%7D%20%7D%7B1.38x10%5E%7B-23%7D%20%2A4.841%7D%20%7D%3D1)
c) If
![\frac{P_{L} }{P_{1} } =e^{-\beta (E_{2}-E_{1} } =ex^{-\frac{\epsilon }{kT} } \\E_{2}-E_{1} =2\epsilon -\epsilon = \epsilon \\Then\\\frac{P_{L} }{P_{1} } = 1 (same)](https://tex.z-dn.net/?f=%5Cfrac%7BP_%7BL%7D%20%7D%7BP_%7B1%7D%20%7D%20%3De%5E%7B-%5Cbeta%20%28E_%7B2%7D-E_%7B1%7D%20%20%7D%20%3Dex%5E%7B-%5Cfrac%7B%5Cepsilon%20%7D%7BkT%7D%20%7D%20%5C%5CE_%7B2%7D-E_%7B1%7D%20%3D2%5Cepsilon%20-%5Cepsilon%20%3D%20%5Cepsilon%20%20%5C%5CThen%5C%5C%5Cfrac%7BP_%7BL%7D%20%7D%7BP_%7B1%7D%20%7D%20%3D%201%20%28same%29)