Answer:
The pressure upstream and downstream of a shock wave are related as

where,
= Specific Heat ratio of air
M = Mach number upstream
We know that 
Applying values we get

Similarly the temperature downstream is obtained by the relation
![\frac{T_{1}}{T_{o}}=\frac{[2\gamma M^{2}-(\gamma -1)][(\gamma -1)M^{2}+2]}{(\gamma +1)^{2}M^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7BT_%7B1%7D%7D%7BT_%7Bo%7D%7D%3D%5Cfrac%7B%5B2%5Cgamma%20M%5E%7B2%7D-%28%5Cgamma%20-1%29%5D%5B%28%5Cgamma%20-1%29M%5E%7B2%7D%2B2%5D%7D%7B%28%5Cgamma%20%2B1%29%5E%7B2%7DM%5E%7B2%7D%7D)
Applying values we get
![\frac{T_{1}}{423}=\frac{[2\times 1.4\times 1.8^{2}-(1.4-1)][(1.4-1)1.8^{2}+2]}{(1.4+1)^{2}\times 1.8^{2}}\\\\\therefore \frac{T_{1}}{423}=1.53\\\\\therefore T_{1}=647.85K=374.85^{o}C](https://tex.z-dn.net/?f=%5Cfrac%7BT_%7B1%7D%7D%7B423%7D%3D%5Cfrac%7B%5B2%5Ctimes%201.4%5Ctimes%201.8%5E%7B2%7D-%281.4-1%29%5D%5B%281.4-1%291.8%5E%7B2%7D%2B2%5D%7D%7B%281.4%2B1%29%5E%7B2%7D%5Ctimes%201.8%5E%7B2%7D%7D%5C%5C%5C%5C%5Ctherefore%20%5Cfrac%7BT_%7B1%7D%7D%7B423%7D%3D1.53%5C%5C%5C%5C%5Ctherefore%20T_%7B1%7D%3D647.85K%3D374.85%5E%7Bo%7DC)
The Mach number downstream is obtained by the relation

Answer:
a) The flow has three dimensions (3 coordinates).
b) ∇V = 0 it is a incompressible flow.
c) ap = (16/3) i + (32/3) j + (16/3) k
Explanation:
Given
V = xy² i − (1/3) y³ j + xy k
a) The flow has three dimensions (3 coordinates).
b) ∇V = 0
then
∇V = ∂(xy²)/∂x + ∂(− (1/3) y³)/∂y + ∂(xy)/∂z
⇒ ∇V = y² - y² + 0 = 0 it is a incompressible flow.
c) ap = xy²*∂(V)/∂x − (1/3) y³*∂(V)/∂y + xy*∂(V)/∂z
⇒ ap = xy²*(y² i + y k) - (1/3) y³*(2xy i − y² j + x k) + xy*(0)
⇒ ap = (xy⁴ - (2/3) xy⁴) i + (1/3) y⁵ j + (xy³ - (1/3) xy³) k
⇒ ap = (1/3) xy⁴ i + (1/3) y⁵ j + (2/3) xy³ k
At point (1, 2, 3)
⇒ ap = (1/3) (1*2⁴) i + (1/3) (2)⁵ j + (2/3) (1*2³) k
⇒ ap = (16/3) i + (32/3) j + (16/3) k
Answer:
L = 46.35 m
Explanation:
GIVEN DATA
\dot m = 0.25 kg/s
D = 40 mm
P_1 = 690 kPa
P_2 = 650 kPa
T_1 = 40° = 313 K
head loss equation
![[\frac{P_1}{\rho} +\alpha \frac{v_1^2}{2} +gz_1] -[\frac{P_2}{\rho} +\alpha \frac{v_2^2}{2} +gz_2] = h_l +h_m](https://tex.z-dn.net/?f=%5B%5Cfrac%7BP_1%7D%7B%5Crho%7D%20%2B%5Calpha%20%5Cfrac%7Bv_1%5E2%7D%7B2%7D%20%2Bgz_1%5D%20-%5B%5Cfrac%7BP_2%7D%7B%5Crho%7D%20%2B%5Calpha%20%5Cfrac%7Bv_2%5E2%7D%7B2%7D%20%2Bgz_2%5D%20%3D%20h_l%20%2Bh_m)
where

density is constant

head is same so,
curvature is constant so
neglecting minor losses

we know
is given as


therefore


V = 25.90 m/s

for T = 40 Degree, 

Re = 4.16*10^5 > 2300 therefore turbulent flow
for Re =4.16*10^5 , f = 0.0134
Therefore



L = 46.35 m
Answer:
The work required is W = 20.2 BTU per lbm
Explanation:
The value of entropy & enthalpy at initial conditions are
= 103.1
S = 0.225
Final enthalpy
= 123.3
Therefore work done
W =
-
W = 103.1 - 123.3
W = - 20.2 BTU per lbm
Therefore the work required is W = 20.2 BTU per lbm