Answer:
Explanation:
Initial conditions


Final conditions


Steady flow energy equation
![\dot{m}\left [ h_1+\frac{v_1^2}{2}+gz_1\right ]+\dot{Q}=\dot{m}\left [ h_2+[tex]\frac{v_2^2}{2}+gz_2\right ]+\dot{W}](https://tex.z-dn.net/?f=%5Cdot%7Bm%7D%5Cleft%20%5B%20h_1%2B%5Cfrac%7Bv_1%5E2%7D%7B2%7D%2Bgz_1%5Cright%20%5D%2B%5Cdot%7BQ%7D%3D%5Cdot%7Bm%7D%5Cleft%20%5B%20h_2%2B%5Btex%5D%5Cfrac%7Bv_2%5E2%7D%7B2%7D%2Bgz_2%5Cright%20%5D%2B%5Cdot%7BW%7D)
![\dot{m}\left [ c_pT_1+\frac{0^2}{2}+g0\right ]+\dot{Q}=\dot{m}\left [ c_pT_2+\frac{0^2}{2}+g0\right ]+\dot{W}](https://tex.z-dn.net/?f=%5Cdot%7Bm%7D%5Cleft%20%5B%20c_pT_1%2B%5Cfrac%7B0%5E2%7D%7B2%7D%2Bg0%5Cright%20%5D%2B%5Cdot%7BQ%7D%3D%5Cdot%7Bm%7D%5Cleft%20%5B%20c_pT_2%2B%5Cfrac%7B0%5E2%7D%7B2%7D%2Bg0%5Cright%20%5D%2B%5Cdot%7BW%7D)
![\dot{m}c_p\left [ T_1-T_2\right ]+\left [ -5hp\right ]=\dot{W} -5\times 746\times 3.4121](https://tex.z-dn.net/?f=%5Cdot%7Bm%7Dc_p%5Cleft%20%5B%20T_1-T_2%5Cright%20%5D%2B%5Cleft%20%5B%20-5hp%5Cright%20%5D%3D%5Cdot%7BW%7D%20-5%5Ctimes%20746%5Ctimes%203.4121)
![-4\dot{m}-\dot{m}\times 0.24\times \left [ 400-60\right ]](https://tex.z-dn.net/?f=-4%5Cdot%7Bm%7D-%5Cdot%7Bm%7D%5Ctimes%200.24%5Ctimes%20%5Cleft%20%5B%20400-60%5Cright%20%5D)



Explanation:
Step1
Strength is the maximum stress induces in the material under applied load condition. More the strength more will be ability to sustain load. Strength can be measured from tensile test. It has same unit as stress. Generally ductile material has more strength as compare to brittle material.
Step2
Hardness is the resistance to scratch on the material under given load condition. More the hardness more will be the resistance towards scratching of material. Hardness can be measured by Rockwell or Birnell hardness test. This property of metal is opposite to the strength.
Step3
Toughness is the ability to absorb energy under given loading condition up to its fracture point. It is a type of strain energy that is stored in the metal. Generally ductile metal has more toughness as compare to brittle.
Complete Question
Consider a single crystal of some hypothetical metal that has the BCC crystal structure and is oriented such that a tensile stress is applied along a [121] direction. If slip occurs on a (101) plane and in a [111] direction, compute the stress at which the crystal yields if its critical resolved shear stress is 2.9 MPa.
Answer:
The stress is 
Explanation:
From the question we are told that
The critical yield resolved shear stress is 
First we obtain the angle
between the slip direction [121] and [111]
![\lambda = cos^{-1} [\frac{(u_1 u_2 + v_1 v_2 + w_1 w_2}{\sqrt{u_1^2 + v_1 ^2+ w_1^2})\sqrt{( u_2^2 + v_2^2 + w_2 ^2)} } ]](https://tex.z-dn.net/?f=%5Clambda%20%3D%20cos%5E%7B-1%7D%20%5B%5Cfrac%7B%28u_1%20u_2%20%2B%20v_1%20v_2%20%2B%20w_1%20w_2%7D%7B%5Csqrt%7Bu_1%5E2%20%2B%20v_1%20%5E2%2B%20w_1%5E2%7D%29%5Csqrt%7B%28%20u_2%5E2%20%2B%20v_2%5E2%20%2B%20w_2%20%5E2%29%7D%20%7D%20%20%5D)
Where
are the directional indices
![\lambda = cos ^-[ \frac{(1) (-1) + (2) (1) + (1) (1)}{\sqrt{((1)^2 +(2)^2 + (1)^2)}\sqrt{((-1)^2 + (1)^2 + (1)^2 ) } } ]](https://tex.z-dn.net/?f=%5Clambda%20%20%3D%20%20cos%20%5E-%5B%20%5Cfrac%7B%281%29%20%28-1%29%20%2B%20%282%29%20%281%29%20%2B%20%281%29%20%281%29%7D%7B%5Csqrt%7B%28%281%29%5E2%20%2B%282%29%5E2%20%2B%20%281%29%5E2%29%7D%5Csqrt%7B%28%28-1%29%5E2%20%2B%20%281%29%5E2%20%2B%20%281%29%5E2%20%29%20%7D%20%20%7D%20%5D)
![= cos^{-1} [\frac{2}{\sqrt{6} \sqrt{3} } ]](https://tex.z-dn.net/?f=%3D%20cos%5E%7B-1%7D%20%5B%5Cfrac%7B2%7D%7B%5Csqrt%7B6%7D%20%5Csqrt%7B3%7D%20%20%7D%20%5D)
Next is to obtain the angle
between the direction [121] and [101]
![\O = cos^{-1} [\frac{(u_1 u_3 + v_1 v_3 + w_1 w_3}{\sqrt{u_1^2 + v_1 ^2+ w_1^2})\sqrt{( u_3^2 + v_3^2 + w_3 ^2)} } ]](https://tex.z-dn.net/?f=%5CO%20%3D%20cos%5E%7B-1%7D%20%5B%5Cfrac%7B%28u_1%20u_3%20%2B%20v_1%20v_3%20%2B%20w_1%20w_3%7D%7B%5Csqrt%7Bu_1%5E2%20%2B%20v_1%20%5E2%2B%20w_1%5E2%7D%29%5Csqrt%7B%28%20u_3%5E2%20%2B%20v_3%5E2%20%2B%20w_3%20%5E2%29%7D%20%7D%20%20%5D)
Substituting 1 for
, 2 for
, 1 for
, 1 for
, 0 for
, and 1 for 
![\O = cos^{-1} [\frac{1* 1 + 2*0 + 1*1 }{\sqrt{1^2 + 2^2 + 1^2 } \sqrt{(1^2 + 0^2 + 1^2 )} } ]](https://tex.z-dn.net/?f=%5CO%20%3D%20cos%5E%7B-1%7D%20%5B%5Cfrac%7B1%2A%201%20%2B%202%2A0%20%2B%201%2A1%20%7D%7B%5Csqrt%7B1%5E2%20%2B%202%5E2%20%2B%201%5E2%20%7D%20%5Csqrt%7B%281%5E2%20%2B%200%5E2%20%2B%201%5E2%20%29%7D%20%20%7D%20%5D)
![\O = cos^{-1} [\frac{2}{\sqrt{6} \sqrt{2} } ]](https://tex.z-dn.net/?f=%5CO%20%3D%20cos%5E%7B-1%7D%20%5B%5Cfrac%7B2%7D%7B%5Csqrt%7B6%7D%20%5Csqrt%7B2%7D%20%20%7D%20%5D)

The stress is mathematically represented as




The answer is memory i believe