I am not sure I am stuck on this and I have been for 45 min someone please help me and this girl or boy!!
Answer:
Time of concentration,
⇒ 1280 min
Peak runoff rate,
⇒4.185 ff³/s
Explanation:
See detailed explanation
Answer:
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if I am right then make me brainliest
Solution :
i. Slip plane (1 1 0)
Slip direction -- [1 1 1]
Applied stress direction = ( 1 0 0 ]
τ = 50 MPa ( Here slip direction must be perpendicular to slip plane)
τ = σ cos Φ cos λ
![$\cos \phi = \frac{(1,0,0) \cdot (1,1,0)}{1 \times \sqrt2}$](https://tex.z-dn.net/?f=%24%5Ccos%20%5Cphi%20%3D%20%5Cfrac%7B%281%2C0%2C0%29%20%5Ccdot%20%281%2C1%2C0%29%7D%7B1%20%5Ctimes%20%5Csqrt2%7D%24)
![$=\frac{1}{\sqrt2 }$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1%7D%7B%5Csqrt2%20%7D%24)
![$\cos \lambda = \frac{(1,0,0) \cdot (1,-1,1)}{1 \times \sqrt3}$](https://tex.z-dn.net/?f=%24%5Ccos%20%5Clambda%20%3D%20%5Cfrac%7B%281%2C0%2C0%29%20%5Ccdot%20%281%2C-1%2C1%29%7D%7B1%20%5Ctimes%20%5Csqrt3%7D%24)
![$=\frac{1}{\sqrt3 }$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1%7D%7B%5Csqrt3%20%7D%24)
τ = σ cos Φ cos λ
∴ ![$50= \sigma \times \frac{1}{\sqrt2} \times \frac{1}{\sqrt3} $](https://tex.z-dn.net/?f=%2450%3D%20%5Csigma%20%5Ctimes%20%5Cfrac%7B1%7D%7B%5Csqrt2%7D%20%5Ctimes%20%5Cfrac%7B1%7D%7B%5Csqrt3%7D%20%24)
σ = 122.47 MPa
ii. Slip plane --- (1 1 0)
Slip direction -- [1 1 1]
![$\cos \phi = \frac{(1, 0, 0) \cdot (1, -1, 0)}{1 \times \sqrt2} =\frac{1}{\sqrt2}$](https://tex.z-dn.net/?f=%24%5Ccos%20%5Cphi%20%3D%20%5Cfrac%7B%281%2C%200%2C%200%29%20%5Ccdot%20%281%2C%20-1%2C%200%29%7D%7B1%20%5Ctimes%20%5Csqrt2%7D%20%3D%5Cfrac%7B1%7D%7B%5Csqrt2%7D%24)
![$\cos \lambda = \frac{(1, 0, 0) \cdot (1, 1, -1)}{1 \times \sqrt3} =\frac{1}{\sqrt3}$](https://tex.z-dn.net/?f=%24%5Ccos%20%5Clambda%20%3D%20%5Cfrac%7B%281%2C%200%2C%200%29%20%5Ccdot%20%281%2C%201%2C%20-1%29%7D%7B1%20%5Ctimes%20%5Csqrt3%7D%20%3D%5Cfrac%7B1%7D%7B%5Csqrt3%7D%24)
τ = σ cos Φ cos λ
∴ ![$50= \sigma \times \frac{1}{\sqrt2} \times \frac{1}{\sqrt3} $](https://tex.z-dn.net/?f=%2450%3D%20%5Csigma%20%5Ctimes%20%5Cfrac%7B1%7D%7B%5Csqrt2%7D%20%5Ctimes%20%5Cfrac%7B1%7D%7B%5Csqrt3%7D%20%24)
σ = 122.47 MPa
iii. Slip plane --- (1 0 1)
Slip direction --- [1 1 1]
![$\cos \phi = \frac{(1, 0, 0) \cdot (1, 0, 1)}{1 \times \sqrt2} =\frac{1}{\sqrt2}$](https://tex.z-dn.net/?f=%24%5Ccos%20%5Cphi%20%3D%20%5Cfrac%7B%281%2C%200%2C%200%29%20%5Ccdot%20%281%2C%200%2C%201%29%7D%7B1%20%5Ctimes%20%5Csqrt2%7D%20%3D%5Cfrac%7B1%7D%7B%5Csqrt2%7D%24)
![$\cos \lambda = \frac{(1, 0, 0) \cdot (1, 1, -1)}{1 \times \sqrt3} =\frac{1}{\sqrt3}$](https://tex.z-dn.net/?f=%24%5Ccos%20%5Clambda%20%3D%20%5Cfrac%7B%281%2C%200%2C%200%29%20%5Ccdot%20%281%2C%201%2C%20-1%29%7D%7B1%20%5Ctimes%20%5Csqrt3%7D%20%3D%5Cfrac%7B1%7D%7B%5Csqrt3%7D%24)
τ = σ cos Φ cos λ
∴ ![$50= \sigma \times \frac{1}{\sqrt2} \times \frac{1}{\sqrt3} $](https://tex.z-dn.net/?f=%2450%3D%20%5Csigma%20%5Ctimes%20%5Cfrac%7B1%7D%7B%5Csqrt2%7D%20%5Ctimes%20%5Cfrac%7B1%7D%7B%5Csqrt3%7D%20%24)
σ = 122.47 MPa
iv. Slip plane -- (1 0 1)
Slip direction ---- [1 1 1]
![$\cos \phi = \frac{(1, 0, 0) \cdot (1, 0, -1)}{1 \times \sqrt2}=\frac{1}{\sqrt2}$](https://tex.z-dn.net/?f=%24%5Ccos%20%5Cphi%20%3D%20%5Cfrac%7B%281%2C%200%2C%200%29%20%5Ccdot%20%281%2C%200%2C%20-1%29%7D%7B1%20%5Ctimes%20%5Csqrt2%7D%3D%5Cfrac%7B1%7D%7B%5Csqrt2%7D%24)
![$\cos \lambda = \frac{(1, 0, 0) \cdot (1, -1, 1)}{1 \times \sqrt3} =\frac{1}{\sqrt3}$](https://tex.z-dn.net/?f=%24%5Ccos%20%5Clambda%20%3D%20%5Cfrac%7B%281%2C%200%2C%200%29%20%5Ccdot%20%281%2C%20-1%2C%201%29%7D%7B1%20%5Ctimes%20%5Csqrt3%7D%20%3D%5Cfrac%7B1%7D%7B%5Csqrt3%7D%24)
τ = σ cos Φ cos λ
∴ ![$50= \sigma \times \frac{1}{\sqrt2} \times \frac{1}{\sqrt3} $](https://tex.z-dn.net/?f=%2450%3D%20%5Csigma%20%5Ctimes%20%5Cfrac%7B1%7D%7B%5Csqrt2%7D%20%5Ctimes%20%5Cfrac%7B1%7D%7B%5Csqrt3%7D%20%24)
σ = 122.47 MPa
∴ (1, 0, -1). (1, -1, 1) = 1 + 0 - 1 = 0