methanol container in a large tank under a pressure 3.5 bar absolute . when the
ID: 2998399 • Letter: M
Question
methanol container in a large tank under a pressure 3.5 bar absolute . when the value on the bottom of the tank is opened, the methanol drained freely through a 1cm ID tube those outlet is 7m below the surface of the methanol.The pressure at the outket of the discharged pipe is 1 atm.
a)Use the bernoulli equation to estimate the methanol discharge velocity and the flow rate in L/min when the value is fully opened.
b) whe the dicharged value is partially closed , the flow rate decreases, which means that delta U^2 /2 changes. however the other two terms in the bernoulli equation ( delta P/density and g delta z) remain the same . How do you account for this apparently contradictory result ?
Explanation / Answer
P1 = 3.5 bar
P2 = Patm
Applying bernoullis equation between top of tank and exit point
P1/pg + v1^2/2g + z1 = P2 + v2^2/2g + z2
P1/pg + z1 = P2 +v2^2/2g neglecting velocity of water in tank
3.5*10^5/9800 + 7 = 1.01325*10^5/9800 + v2^2/2g
Discharge velocity, v2 = 25.19 m/s
Flow rate = v2*area
= 25.19 *pi*0.01^2/4
= 1.9784 *10^-3 m3/s
= 1.9784 L/s
Flow rate = 118.70 L/min
when the discharge valve is partially closed, area of flow reduces which reduces flow rate.
velocity of flow remains same.
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