Determine the pressure difference in a tube o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) $1$. Apply the equation of continuity: $A_{1} v_{1} = A_{2} v_{2}$.Since $A = \pi (d/2)^{2}$,we have $d_{1}^{2} v_{1} = d_{2}^{2} v_{2}$.Substitut

Vedclass · Accepted Answer

$304500$

Vedclass · Answer

(B) $1$. Apply the equation of continuity: $A_{1} v_{1} = A_{2} v_{2}$.Since $A = \pi (d/2)^{2}$,we have $d_{1}^{2} v_{1} = d_{2}^{2} v_{2}$.Substituting the values: $5^{2} 	imes 4 = 2^{2} 	imes v_{2} \implies 25 	imes 4 = 4 	imes v_{2} \implies v_{2} = 25 \, m/s$.$2$. Apply Bernoulli's equation (assuming horizontal flow): $P_{1} + \frac{1}{2} ho v_{1}^{2} = P_{2} + \frac{1}{2} ho v_{2}^{2}$.$3$. Rearrange to find the pressure difference $\Delta P = P_{1} - P_{2} = \frac{1}{2} ho (v_{2}^{2} - v_{1}^{2})$.$4$. Substitute the values: $\Delta P = \frac{1}{2} 	imes 1000 	imes (25^{2} - 4^{2})$.$\Delta P = 500 	imes (625 - 16) = 500 	imes 609 = 304500 \, Pa$.

Column - $I$	Column - $II$
$(a)$ Velocity head	$(i)$ $\frac{P}{\rho g}$
$(b)$ Pressure head	$(ii)$ $h$
$(c)$ Potential head	$(iii)$ $\frac{v^2}{2g}$

Determine the pressure difference in a tube of non-uniform cross-sectional area as shown in the figure. $\Delta P = ?$ (in $Pa$)
$d_{1} = 5 \, cm, V_{1} = 4 \, m/s, d_{2} = 2 \, cm, V_{2} = ?$
Assume the fluid is water with density $\rho = 1000 \, kg/m^{3}$.

Similar Questions

The lift of an airplane is based on

Different heads are in Column - $I$ and their formulas are given in Column - $II$. Match them appropriately.
Column - $I$ Column - $II$
$(a)$ Velocity head $(i)$ $\frac{P}{\rho g}$
$(b)$ Pressure head $(ii)$ $h$
$(c)$ Potential head $(iii)$ $\frac{v^2}{2g}$

Water is filled in a cylindrical container to a height of $3 \ m$. The ratio of the cross-sectional area of the orifice and the beaker is $0.1$. The square of the speed of the liquid coming out from the orifice is ....... $m^2/s^2$ $(g = 10 \ m/s^2)$.

Consider the following equation of Bernoulli's theorem: $P + \frac{1}{2}\rho V^2 + \rho gh = K$ (constant). The dimensions of $K/P$ are the same as those of which of the following?

What is a venturi meter?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Determine the pressure difference in a tube of non-uniform cross-sectional area as shown in the figure. $\Delta P = ?$ (in $Pa$)$d_{1} = 5 \, cm, V_{1} = 4 \, m/s, d_{2} = 2 \, cm, V_{2} = ?$Assume the fluid is water with density $\rho = 1000 \, kg/m^{3}$.