Waster flows throgh a horizontal tube of variable cross section.The area of cross section at A and B are 4 `mm^2 and 2mm^2` respectively. If 1 cc of water enters per seconds through. A find a. The speed of water at A, b. the speed of river at B and c. the pressure difference `P_A-P_B`.

Answer

A, B, C, D

Explanation

a. Given
`Q_A/t=(1a)/sec=discharge
`rarr a_AxxV_A=Q_A`
`rarr 4xx10^-2xxV_a=cc/sec`
[because `a_A4m^2=4xx10^-o2cm^2]`
`V_A=25m/sec`
b. `a_Axxv_A=a_BxxV_B`
`rarr 4x10^-2xx25=4xx10^-2xxV_B`
`rarr V_B=50cm/sec`
c. From Bernoulli's equation
`1/2rhov_A^2+rh0_A=1/2rhov_B^2+rho_B`
`rarr (P_A-P_B)=1/2rho(v_B^2-v_A^2)`
`=1/2xx1xx(250-625)`
` =1875/2`
`=937.5 Dyne/cm^2`
`=93.75N/m^2`
`=94N/m^2`